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The graph of $y = f(x)$ is shown below. Assume the domain of $f$ is $[-4,4]$ and that the vertical spacing of grid lines is the same as the horizontal spacing of grid lines.

 

 

Part (a): The points $(a,4)$ and $(b,-4)$ are on the graph of $y = f( 2x).$ Find $a$ and $b.$

 

Part (b): Find the graph of $y = f(2x).$ Verify that your points from part (a) are on the graph.

 

Part (c): The points $(c,4)$ and $(d,-4)$ are on the graph of $y = f(2x-8).$ Find $c$ and $d.$

 

Part (d): Find the graph of $y = f(2x - 8).$ Be sure to verify that your points from part (c) are on the graph both algebraically and geometrically.

 Mar 24, 2019

Best Answer 

 #1
avatar+533 
+1

a)

Let's first find the points that are on y = f(x). This means the y coordinates are 4 and -4, so the x's are -4 and 4, respectively. Because it is on the graph of f(2x), the 2x halves the values, giving a = -2 and b = 2.

 

b)

Since I can't draw it out, I will tell you how to draw it. 

f(2x) will need a half as small x value to have the same effect. Here's an example: f(2 * 3) = f(6). So, we just have to "squish" the graph in towards the linex = 0 so that each x coordinate is half as much, but the y coordinates are the same.

 

c)

We know that the x's are -4 and 4 (from (a)). So, we set 2x - 8 equal to -4 and 4, getting c = 2 and d = 6.

 

d)

It has the same coefficient of x, so you can just draw graph b with the same shape but have (2, 4) and (-4, 6) and on the graph in the same spots that (-2, 4) and (2, -4) were in the graph of f(2x).

 Mar 24, 2019
 #1
avatar+533 
+1
Best Answer

a)

Let's first find the points that are on y = f(x). This means the y coordinates are 4 and -4, so the x's are -4 and 4, respectively. Because it is on the graph of f(2x), the 2x halves the values, giving a = -2 and b = 2.

 

b)

Since I can't draw it out, I will tell you how to draw it. 

f(2x) will need a half as small x value to have the same effect. Here's an example: f(2 * 3) = f(6). So, we just have to "squish" the graph in towards the linex = 0 so that each x coordinate is half as much, but the y coordinates are the same.

 

c)

We know that the x's are -4 and 4 (from (a)). So, we set 2x - 8 equal to -4 and 4, getting c = 2 and d = 6.

 

d)

It has the same coefficient of x, so you can just draw graph b with the same shape but have (2, 4) and (-4, 6) and on the graph in the same spots that (-2, 4) and (2, -4) were in the graph of f(2x).

asdf335 Mar 24, 2019

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