The graph of 
is shown below. Assume the domain of 
is ![[-4,4]](/api/ssl-img-proxy?src=https%3A%2F%2Fdata.artofproblemsolving.com%2Fimages%2Flatex%2F3%2F2%2F2%2F322e7229ba5e3563baa460fc6301f88fe3875ab7.gif "[-4,4]")
and that the vertical spacing of grid lines is the same as the horizontal spacing of grid lines. 
Part (a): The points 
and 
are on the graph of 
Find 
and 
Part (b): Find the graph of Verify that your points from part (a) are on the graph.
Part (c): The points 
and 
are on the graph of 
Find 
and 
Part (d): Find the graph of Be sure to verify that your points from part (c) are on the graph both algebraically and geometrically.
This week, it is important that your submission includes graphs.
hints:
and 
+23254 For the graph shown, each box has a width and height of 1.
The graph of f(2x) would be identical to the graph of f(x) if you change the scale on the x-axis, so that the width of each box would be ½ (but keep the height the same as it was).
a) On the original graph, there is the point (-4, 4). On the graph of f(2x), the coordinates of the point are (-2,4), so a = -2.
On the original graph, there is the point (4, -4). On the graph of f(2x), the coordinates of the point are (2, -4), so b = 2.
b) See the note above part a.
c) f(2x - 8) = f( 2(x - 4) ) This graph makes a horizontal shift of the graph of f(2x) 4 spaces to the right. The graph of f(2x - 8), which is f( 2(x - 4) ), is congruent to the graph of f(2x), just move it 4 spaces to the right.
Moving (-2,4) four spaces to the right creates (2,4), so c = 2.
Moving (2,-4) four spaces to the right creates (6, -4), so d = 6.
d) Draw the graph of f(2x), then move that graph 4 spaces to the right to create f(2x - 8).
+23254 For the graph shown, each box has a width and height of 1.
The graph of f(2x) would be identical to the graph of f(x) if you change the scale on the x-axis, so that the width of each box would be ½ (but keep the height the same as it was).
a) On the original graph, there is the point (-4, 4). On the graph of f(2x), the coordinates of the point are (-2,4), so a = -2.
On the original graph, there is the point (4, -4). On the graph of f(2x), the coordinates of the point are (2, -4), so b = 2.
b) See the note above part a.
c) f(2x - 8) = f( 2(x - 4) ) This graph makes a horizontal shift of the graph of f(2x) 4 spaces to the right. The graph of f(2x - 8), which is f( 2(x - 4) ), is congruent to the graph of f(2x), just move it 4 spaces to the right.
Moving (-2,4) four spaces to the right creates (2,4), so c = 2.
Moving (2,-4) four spaces to the right creates (6, -4), so d = 6.
d) Draw the graph of f(2x), then move that graph 4 spaces to the right to create f(2x - 8).
