Shifting and Reflecting Graphs

1) Which common graph would you use to help graph the function g(x) = x² – 3

2) Compared to the graph of its common function, describe the transformation of the following: g(x) = -x² + 2

a. Reflected with respect to x-axis, translated right 2 units.

b. Reflected with respect to x-axis, translated left 2.

c. Reflected with respect to x-axis, translated up 2.

d. Reflected with respect to x-axis, translated down 2.

3) Compared to the graph of its common function, describe the transformation of the following: g(x) =

a. translated three units left and two units up.

b. translated three units right and two units up.

c. translated two units right and three units down

d. translated two units right and three units up.

4) Compared to the graph of its common function, describe the transformation of the following: g(x) = |x + 3| ­- 1

a. translated three units left and one unit down.

b. translated three units right and one unit down.

c. translated one unit left and three units up.

d. translated one unit left and three units down.

5) The following graph shows a transformation of the function f(x) = x^2. Which function shows g(x), the equation of the transformed graph?

a. g(x) = -(x+2)² +2

b. g(x) = -(x-2)² -2

c. g(x) = -(x-2)² +2

d. g(x) = -(x+2)² -2

6) Find f(x – 1) + 2 for the graph, f(x), shown below.

a.

c.

d.

7) Find f(x – 4) + 1 for the graph, f(x), shown below.

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