Intro to Transformations of Functions

Using your calculator, graph the function f(x) = |x+2|, then compare to the parent function. Which of the following describes the transformation?

• The graph is shifted 2 units to the left.

• The graph is shifted 2 units to the right.

• The graph is shifted 2 units up.

• The graph is shifted 2 units down.

Using your calculator, graph the function f(x) = |x−2|, then compare to the parent function. Which of the following best describes the transformation from the parent function f(x) = |x|?

• The graph is shifted 2 units to the right.

• The graph is shifted 2 units to the left.

• The graph is shifted 2 units up.

• The graph is shifted 2 units down.

Using your calculator, graph the function f(x) = |x|+2, then compare to the parent function. Which of the following describes the transformation?

• The graph is shifted 2 units up.

• The graph is shifted 2 units down.

• The graph is shifted 2 units to the left.

• The graph is shifted 2 units to the right.

Using your calculator, graph the function f(x) = |x|−2, then compare to the parent function. Which of the following describes the transformation?

• The graph is shifted 2 units up.

• The graph is shifted 2 units down.

• The graph is shifted 2 units to the right.

• The graph is shifted 2 units to the left.

What is the effect on the graph of the linear parent function, f(x) = x, when f(x) is replaced by f(x- 7)? Complete the sentence by selecting the correct answers from the drop-down menus. The graph of the line ​ (a)   ​ ​ (b)   7 units.

• shifts horizontally

• up

• down

• left

• right

• shifts vertically

The linear parent function, f(x) = x, is transformed to g(x) = f(x + 3). Describe the transformation. (a)  

• g(x) is shifted up 3 units

• g(x) is shifted down 3 units

• g(x) is shifted left 3 units

• g(x) is shifted right 3 units

• horizontally

• vertically

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation. (a)  

• g(x) is shifted up 6 units

• g(x) is shifted down 6 units

• g(x) is shifted left 6 units

• g(x) is shifted right 6 units

Rewrite f(x) = 2x - 1 shifted up three units and the slope doubled (a)  

• f(x) = 5x - 2

• f(x) = 4x + 2

• f(x) = 4x + 3

• f(x) = 5x - 4

• Flip

• Vertical Compression

• Same as

• Vertical Stretch

• Horizontal Stretch

• Horizontal Compression

• (-4,-1)

• (4,1)