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# help pls (repost because the original never got answered)

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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

#1
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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
+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).

asdf335 Mar 24, 2019