F(x)=2|x-1| Graph using transformations and describe the transformations of the parent function y =x^2.
Answers
[Please see that in the question should be a mistake regarding the parent function. It should be written y = |x| instead of y = x².]
To answer this question, we need to know that the below function is a transformation of the parent function, f(x) = |x|:
[tex]f(x)=2|x-1|[/tex]Describing the transformationsTo end up with the above function from the parent function, we need to follow the next steps:
1. Translate the function, y = |x| one unit to right. We can do this by subtracting one unit to the parent function as follows:
[tex]f(x)=|x-1|[/tex]We can see this graphically as follows:
The blue function is the first transformation of the parent function, f(x) = |x|.
2. The function has been dilated by a factor of 2 from the x-axis. That is, the function has been dilated by a factor of 2 vertically. Then, we have:
[tex]f(x)=2|x-1|[/tex]And now, we can see the transformation graphically as follows:
Therefore, the blue line is the graph representation of the function:
[tex]f(x)=2|x-1|[/tex]
Related Questions
use the graph of the table of the parabola to fill in thetable
Answers
Given:
The graph of a parabola is given
Required:
Where does the parabola open
The co-ordinate of the vertex
The intercepts
The equation of line of symmetry
Explanation:
a) As we can see the parabola faces downwards
b) The vertex represents the highest point of the circle here. As we cab see, this is the point through which the axis of symmetry passes through to make a symmetrical division of the parabola.
We have the co-ordinates of this point as (-1, 9)
c) The x-intercepts are the two points in which the parabola crosses the x- axis
From the graph, we have the points as 2 and -4
So the x-intercepts are at the points (2, 0) and (-4, 0)
For y- intercept, it is the y co-ordinate of the point at which the parabola crosses the y- axis and the point is (0, 8)
d) To find the axis of symmetry equation, we look at the graph and see the point through the vertex of the parabola that exactly divides the parabola into two equal parts.
The x-value that the line passes through here is the point x = -1 and this is the equation of symmetry.
Final answer:
a) Downwards
b) (-1, 9)
c) x- intercept: (2, 0), (-4, 0)
y-intercept: (0, 8)
d) x= -1
- Describe at least one thing you would do to critique Mary's reasoning.
Answers
Process to critique the reasoning of others is to clarifying the question.
A critique is to evaluate somebody's work (a book, an essay, a movie, a painting...) in order to increase the reader's understanding of it.
A critical analysis is subjective writing because it expresses the writer's opinion or evaluation of a text. Analysis means to break down and study the parts.
Writing a critical paper requires two steps: critical reading and critical writing.
Process to critique the reasoning of others.
Ask clarifying questions as someone explains their plan to solve the problem. Ask clarifying questions as someone explains their answer and how they solved the problem. Cite similarities and differences between strategies for how the problem could be solved.
Hence the answer is the Process to critique the reasoning of others is to clarifying the question.
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A number is chosen at random from 1 to 50. Find the probability of not selecting odd or prime numbers.
Answers
0
Between 1 and 50 are odd and even numbers hence the probability of not selecting an odd or even number is 0
Evaluate the function f(x) = 2x – 2, when x = –1.a.45b.40c.35d.30
Answers
ANSWER
• x = 10.83
,• ∡A = 65º
EXPLANATION
The sum of the measures of the interior angles of any triangle is 180º:
[tex]\measuredangle A+\measuredangle B+\measuredangle C=180º[/tex]Replacing with the angles we know (B and C):
[tex]\measuredangle A+75º+40º=180º[/tex]And solving for ∡A:
[tex]\begin{gathered} \measuredangle A=180º-75º-40º \\ \measuredangle A=65º \end{gathered}[/tex]Then we know that ∡A = 6x, so x is:
[tex]undefined[/tex]ReTest_Linear Functions Unit Topic 35 of 75 of 7 Items25:50 / 01:30:00 Is the relation a function? If so, is it one-to-one or not one-to-one?
Answers
Function
one- to -one
Explanation:For a relation to be a function, each of the input of the function must have only one output.
The input are the x values while the output are the y values.
Input -2 has one output of -1
input -1 has output of -2
input 0 has output 0
input 1 has output 2
input 2 has output 4
Each of the input have only one output.
Hence, it is a function
A function is one-to-one when the elements in the domain has one value in the range.
Hence, it is one-to-one
Steve is going to paint a wall that measures 9 feet by 12 feet. If one gallon of paint is needed for each s square foot of wall and each each gallon costs g dollars, in terms of s and g how much does it cost to paint the entire wall?
Answers
The wall is 9 feet by 12 feet, so its area is given by,
[tex]\begin{gathered} =9\cdot12 \\ =108 \end{gathered}[/tex]So the area of the wall that needs to be painted is 108 square feet.
Given that each 's' square foot required 1 gallon of paint, then the amount of paint required to paint the complete wall will be calculated as,
[tex]\begin{gathered} \because s\text{ sq ft}\equiv1\text{ gallon} \\ \therefore108\text{ sq ft}\equiv\frac{108\cdot1}{s}=\frac{108}{s}\text{ gallons} \end{gathered}[/tex]So the amount of paint required for the whole wall is 108/s gallons.
Given that 1 gallon of paint costs 'g' dollars, the cost of total paint required will be,
[tex]\begin{gathered} \because1\text{ gallon paint}\equiv g\text{ dollars} \\ \therefore\frac{108}{s}\text{ gallons paint}\equiv\frac{(\frac{108}{s})\cdot g}{1}=\frac{108g}{s}\text{ dollars} \end{gathered}[/tex]Thus, the cost (in dollars) of the total paint required for painting the wall is obtained as,
[tex]\frac{108g}{s}[/tex]Therefore, option D is the correct choice.
Question: pitcher of water holds 48.2 ounces of water in it. The water is oured into two glasses, 12.08 ounces into one glass and 18.86 punces into a second glass. 1. How much water is poured out of the pitcher? I 2. How much water is left in the pitcher? Show all Steps to have full credit
Answers
the water in pitcher is 48.2 ounces,
the water poured into one glass is 12.08 ounces
the water poured into another glass is 18.86 ounces
1)
tota water poured into the two glasses is = 12.08 + 18.86 = 30.94 ounces
2)
the water left in the pitcher is 48.20 - 30.94 = 17.26 ounces
The ratio of pumpkins to apples are 3 to 1 if there are 60 pumpkins then how many apples are there.
Answers
Answer:
20 apples
Step-by-step explanation:
For every three pumpkins, there is one apple.
There are 60 pumpkins. Divide 60 by 3 to find how many apples there are.
60 ÷ 3 = 20
Task 2Graphing Proportional RelationshipsGraph each leg of Kiley’s trip with the time (in hours) along the x-axis and the distance (in miles) along the y-axis. First you will answer some questions below to find the correct coordinates to use for your graph. In part H, you will create the graph using this spreadsheet.Part AThe starting coordinates of the graph will be (0, 0), or the origin. This point represents Kiley’s house. From here, if you drew a line segment that represents Kiley’s car ride from her house to the airport, at what point would the line segment end?
Answers
We want to draw a graph with a y-axis equal to the distance from Kiley's home, and the x-axis represents the amount of time the trip will take. Then, each point point on this graph represent a location. Since our origin(0, 0) is Kiley's house, if we drew a line segment that represents Kiley’s car ride from her house to the airport, this line would end at the location of the airport, the y-axis would inform how far is the airport and the x-axis how much time it is needed to get there.
Since Kiley drove 24.3 miles from their house to the airport in 1/2 hour, this means the end of this line will be at (0.5, 24.3).
1000C The formula that relates the wattage of an appliance to the cost to run the appliance is W = 1000/tcwhere W is the wattage of appliance, C is the cost to use the appliance per month, t is the time in hours per month, and c is the cost of electricity per kilowatt hour. Use $0.15 per kilowatt-hour for the cost of electricity. How much does it cost to run a 60-watt light bulb 720 hours a month? A. $0.15 B.$6.48 C.$12.32 D.$288
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Hence, the correct option is Option C
-3, -6, 12, -24,..... Recursive Formula an = an -1 -48an = an -1 . 2an = an -1 - 12an = - 3 . 2n -1
Answers
Answer:
The recursive formula is;
[tex]a_n=a_{n-1}\cdot2[/tex]Explanation:
The recursive formula for geometric progression can be written as;
[tex]a_n=a_{n-1}\cdot r[/tex]where r is the common difference.
Let us find the common difference of the given sequence;
[tex]-3,-6,-12,-24,\ldots[/tex][tex]\begin{gathered} r=\frac{-6}{-3}=\frac{-12}{-6} \\ r=2 \end{gathered}[/tex]we can now substitute the value of r into the recursive formula;
[tex]a_n=a_{n-1}\cdot2[/tex]Therefore, the recursive formula is;
[tex]a_n=a_{n-1}\cdot2[/tex]
A firm makes circular drink mats , of radius 4.5cm , that are 3mm thick . They want to produce a rectangular box to hold a pile of 12 mats. What are the minimum dimensions of the box.
Please answer with working out
please help
its maths level 2 its hard
Answers
The minimum dimensions of the rectangular box will be 9cm by 9cm by 3.6cm or 90mm by 90mm by 36mm
Calculating the dimensions of a rectangular boxTo calculate the dimensions of a rectangular box, firstly measure its length, width, and height using the same units such as millimeters or centimeters for all 3 measurements! Then, multiply the 3 measurements together using Length × Width × Height.
From the question, radius of the circular mat is 4.5cm, hence;
the total length of the mat = 2 × 4.5cm {2radius = diameter}
the total length of the mat = 9cm
The length of the mat is the same around the mat, thus the box has a length of 9cm by width of 9cm.
The height of the rectangular box will be determined by the total thickness of the 12 mats, so;
the thickness of a mat is given as 3mm
thus converting millimeter to centimeter
thickness of a mat = 0.1cm × 3 {as 1mm = 0.1cm}
thickness of a mat = 0.3cm
total thickness of 12 mats = 0.3cm × 12
total thickness of 12 mats = 3.6cm
From our workings, the rectangular box will have a minimum dimension of length 9cm by width 9cm by height 3.6cm or 90mm by 90mm by 36mm.
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How many terms are in the expansion of the binomial below? (x^3 + 2/x)^8A: 9B: 8C: 11D: 10
Answers
Given expression is
[tex](x^3+\frac{2}{x})^8[/tex]This is of the form
[tex](a+b)^n[/tex][tex]\text{where}a=x^3,\text{ b=}\frac{2}{x}\text{ and n=8}[/tex]Recall that
[tex]In\text{ the binomial expansion of }(a+b)^n,\text{ there are total n+1 terms.}[/tex]Here n=8.
[tex]In\text{ the binomial expansion of }(x^3+\frac{2}{x})^8,\text{ there are total 8+1=9 terms.}[/tex]Hence option A is correct.
if f(x)=sinx, then f'(pi/3)=
Answers
Solution
- The function given is
[tex]f(x)=\sin x[/tex]- We are asked to find
[tex]f^{\prime}(\frac{\pi}{3})[/tex]- The differentiation of the sine function gives:
[tex]f^{\prime}(x)=\frac{d}{dx}(\sin x)=\cos x[/tex]- Thus, we can solve the question by simply substituting π/3 into the function f'(x).
- That is,
[tex]\begin{gathered} f^{\prime}(x)=\cos x \\ put\text{ }x=\frac{\pi}{3} \\ \\ \therefore f^{\prime}(\frac{\pi}{3})=\cos\frac{\pi}{3}=\frac{1}{2} \end{gathered}[/tex]Final Answer
The answer is
[tex]f^{\prime}(\frac{\pi}{3})=\frac{1}{2}[/tex]Identify if the function has an odd or even degree and positive or negative leading coefficient.
Answers
In this problem
The end behavior of the function is
f(x)→−∞, as x→−∞
f(x)→−∞, as x→+∞
that means
The degree is even
The leading coefficient is negative
therefore
The answer is even negative3x^4+4x-8How many zeros does the polynomial fiction.
Answers
Given that the degree of the given polynomial is 4, it is possible to have at most 4 zeroes .
Graphing the given polynomial we have
Which suggest that the polynomial has 2 real roots, and at most 2 complex roots.
If a triangle ABC is at: A = (10, 7) B = (4, -4) C= (- 11, -9) and if it is translated right 2 and down 7, find the new point B'
Answers
B' (6, -11)
Explanations:
Translations is a transformation technique used to change the position of an object in an xy-plane.
Given the coordinate of a triangle ABC given as A (10, 7) B (4, -4) C (- 11, -9). If it is translated right 2 and down 7, the translation rule will be;
(x, y) -> (x+2, y-7)
Determine the new point B'
B' = (4+2, -4-7)
B' = (6, -11)
Therefore the coordinate of the new point B' is (6, -11)
A toaster oven usually sells for $61. If the toaster oven is 20% off, and sales tax is 6%, what is the total price of the toaster oven, including tax?
Answers
The total price of the toaster oven, including tax, is $51.7, using a percentage tax.
What is percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The % sign is used to denote it.
The cost of toaster oven is $61.
if It has 20% off it's price
So the price will be 61*20/100 = 12.2
The discounted price is 61-12.2 = $48.8
It will have a tax of 6% Percentage
So the tax will be 48.8*6/100 =$2.9
Now the price of the toaster oven will be 48.8 + 2.9 = $51.7
Hence the total price of the toaster oven, including tax is $51.7
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A 21 oz bottle of dish soap sells for $8.47. A 25 oz bottle of dish soap sells for $9.78.(round all answers to four decimal places)The unit price of the 21 oz bottle is $ per ozThe unit price of the 25 oz bottle is $ per ozWhich of the two is a better deal?
Answers
To find the unit prices, divide the price by the number of ounces, this way:
For the 21oz bottle that costs $8.47:
[tex]\frac{8.47}{21}=0.4033[/tex]The unit price is $0.40 per oz
For the 25oz bottle that cost $9.78:
[tex]\frac{9.78}{25}=0.3912[/tex]The unit price is $0.39 per oz.
It means that the 25oz bottle is a better deal because it has a lower unit price.
Simplify: (5−23+2−7)−(25+74−43+2)
Answers
From the given expression we get:
[tex](x^5-2x^3+x^2-7)-(2x^5+7x^4-4x^3+2)=x^5-2x^3+x^2-7-2x^5-7x^4+4x^3-2[/tex]Associating similar terms we get:
[tex]\begin{gathered} (x^5-2x^5_{})+(-2x^3+4x^3)+(x^2)+(-7-2) \\ =-x^5+2x^3+x^2-9 \end{gathered}[/tex]A bicycle shop rent bicycles by the hour. It charges and equipment fee with every rental. The graph shows the cost of renting a bicycle for different periods of time. Drag numbers to complete a linear function in terms of why equals MX plus E tomorrow the situation. Numbers may be used once, more than once, or not at all.
Answers
y = 15x + 10
Explanation:Given a graph, we use the equation of line y = mx + b
m = slope
b = y-intercept
First let's find the slope using the formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} u\sin g\text{ any two points on the line: } \\ (2,40)\text{ and (4, 70)} \\ x_1=2,y_1=40,x_2=4,y_2\text{ = }70 \\ m\text{ = slope = }\frac{70-40}{4-2} \\ \text{slope = }\frac{30}{2}\text{ = 15} \end{gathered}[/tex]The y-intercept is the value of y when x = 0. It is also the value of y when the line crosses the y-axis.
The value of cost when time is zero
The line crosses the y-axis at y = 10
Hence, the y-intercept is 10
The equation of line becomes:
y = 15x + 10
If the surface area of a sphere is equal to the volume of the sphere, then what is the length of its radius?A. 3 unitsB. 2 unitsC. 0.5 unitsD. 1 unit
Answers
Given:
That the surface area of a sphere is equal to the volume of the sphere.
[tex]\begin{gathered} \text{The surface area of a sphere is given by:} \\ A=4\pi r^2 \\ \\ \text{The volume of a sphere is given by:} \\ V=\frac{4}{3}\pi r^3 \end{gathered}[/tex]If area is equal to volume, then;
[tex]\begin{gathered} A=V \\ 4\pi r^2=\frac{4}{3}\pi r^3 \\ C\text{ ross multiplying,} \\ 4\pi r^2\times3=4\pi r^3 \\ 12\pi r^2=4\pi r^3 \\ \text{Dividing both sides by }4\pi r^2\text{ to get the radius,} \\ \frac{12\pi r^2}{4\pi r^2}=\frac{4\pi r^3}{4\pi r^2} \\ 3=r \\ r=3\text{units} \end{gathered}[/tex]Therefore, the length of the radius is 3units.
The correct answer is option A.
I need help with this question finding cos Y=?the options are the following5/1312/135/12
Answers
Cosy = Adjacent/Hypotanuse
[tex]\begin{gathered} \theta\text{ = y} \\ \text{Opposite = }5 \\ \text{Hypotanuse = 13} \\ \text{Adjacent = 12} \\ \cos y\text{ = }\frac{adjacent}{\text{Hypotanuse}} \\ \cos y\text{ = }\frac{12}{13} \end{gathered}[/tex]Simplify by finding the product of the polynomials below. Then Identify the degree of your answer. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. (2x^2+2x+1)(4x-1) This simplifies to: AnswerThe degree of our simplified answer is: Answer
Answers
Solution:
Given:
[tex](2x^2+2x+1)(4x-1)[/tex]To get the product of the polynomial; we use the distributive property of multiplication.
[tex]a(b+c)=ab+ac[/tex][tex]\begin{gathered} (4x-1)(2x^2+2x+1) \\ 4x(2x^2+2x+1)-1(2x^2+2x+1) \\ =8x^3+8x^2+4x-2x^2-2x-1 \\ \text{Collecting similar terms together and simplifying further;} \\ =8x^3+8x^2-2x^2+4x-2x-1 \\ =8x^3+6x^2+2x-1 \end{gathered}[/tex]Therefore, the product of the polynomials is;
[tex]8x^3+6x^2+2x-1[/tex]Find the value of x . (Do not round until the final answer . Then round to the nearest tenth as needed .)
Answers
According to the given image, x is the radius of the circle.
So, we can find x using Pythagorean's Theorem in the following right triangle.
Where x is the hypothenuse.
[tex]\begin{gathered} x^2=5.3^2+4^2 \\ x=\sqrt[]{28.09+16} \\ x=\sqrt[]{44.09}\approx6.6 \end{gathered}[/tex]Hence, x is 6.6, approximately.two friends race. The first friend gets a head start and runs at a steady rate of 0.20 miles per minute. The second friend waits 1 minute and then runs at a steady rate of 0.25 mi per minute. how long will it take for the second friend to catch up with the first one
Answers
Here, we want to calculate the time in minutes it will take for the second friend to catch up with the first.
What this mean is that how long in minutes will it take for them to have traveled the same distance.
Let the number of minutes be x
Mathematically;
distance = speed * time
So in x minutes, the distance the first friend will have traveled will be;
distance = 0.20 miles per minutes * x minutes = o.
Complete the following by filling in the missing terms in the sequence
Answers
Let's begin with the first sequence:
[tex]?,2,6,18,54,\text{?}[/tex]We can see each term of the sequence after the 2 is the previous term multiplied by 3. So the missing terms would be 2/3 and 54*3:
[tex]\frac{2}{3},2,6,18,54,162.[/tex]For the second sequence, we have:
[tex]?,?,17,12,7,2.[/tex]We can see that after the 17, each term is the previous one minus 5. So the sequence is:
[tex]27,22,17,12,7,2.[/tex]The third and fourth sequences are written correctly in the image.
For the fifth sequence, the only information we have to determine the ruele it's following is that the next number after 9 is 16, and the 1 that is before the number before the 9.
One possible rule would be to consider the sequence
[tex]x_n=n^2\text{.}[/tex]This way, if we start from n=0 we get:
[tex]0,1,4,9,16,25,[/tex]which fits the numbers we were given perfectly.
Question 3 Sandwiches Eaton at Lunch Number of Sandwiches clasematon Tona Choose Peanut butter jelly What is the ratio of classmates who like ham sandwiches to the number of classmates who like bologna and turkey sandwiches? 12
Answers
1 : 2 (option B)
Explanation:Number that liked ham sandwiches = 6
Number that liked bologna = 2
Number that liked Turkey = 10
Total number that liked bologna and Turkey = 2 + 10 = 12
Ratio of ham to bologna and Turkey = Number that liked ham sandwiches : number that liked bologna and Turkey
Ratio of ham to bologna and Turkey = 6 : 12
Ratio of ham to bologna and Turkey = 1 : 2 (option B)
a. an 9. Find the explicit formula for the given sequence. -4,0,4,8,... = 4+ -4(n-1) b. an = – 4 · 8(n − 1) -4 + 4(n − 1) -4 · 4(n-1) c. an d. an
Answers
The given sequence is
-4 , 0 , 4 , 8 , ......
the given sequence is arithmetic sequence
because there is a common difference between the terms of the sequence
common difference = 0 - (-4) = 4
as a check = 4 - 0 = 4 and 8 - 4 = 4
and the first term is -4
So,
The explicit formula is an = a1 + d ( n - 1)
an = -4 + 4 ( n - 1)
The answer is option c
what is the solution to the system of the equation graphed below? type your answer as an ordered pair (x, y)
Answers
To find the solution of a system of equation graphed, it is the point where the two lines crosses with each other
for that we found the equation of the line for both of them using the points given
the slope for the orange line is 1/2
the slope for the green line is 1
the y-intercept for the orange line is 3
the y-intercept for the green line is 1
the equation for the orange line is
[tex]y=\frac{1}{2}x+3[/tex]the equation for the green line is
[tex]y=x+1[/tex]equal both of the equations
[tex]\begin{gathered} x+1=\frac{1}{2}x+3 \\ \frac{1}{2}x=2 \\ x=4 \end{gathered}[/tex]using the equation to find the point where they cross
[tex]\begin{gathered} y=x+1 \\ y=4+1 \\ y=5 \end{gathered}[/tex]the solution of the system is (4,5)