Transformations of Functions Intro

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.

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

• The graph is a vertical stretch of the parent function by a factor of 2.

• The graph is a vertical compression of the parent function by a factor of 2.

• The graph is a horizontal stretch of the parent function by a factor of 2.

• The graph is a horizontal compression of the parent function by a factor of 2.

Using your calculator, graph the function f(x) = 1/2|x|, then compare to the parent function. Which of the following best describes the transformation?

• The graph is a vertical stretch of the parent function.

• The graph is a vertical compression of the parent function.

• The graph is a horizontal stretch of the parent function.

• The graph is a horizontal compression of the parent function.

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

• The graph is a reflection of the parent function across the x-axis.

• The graph is a vertical stretch of the parent function.

• The graph is a horizontal shift of the parent function.

• The graph is a vertical shift of the parent function.

What is the parent function of an absolute equation?

• y = x

• y = |x|

• y = x^2

• y = 1/x

Which of the following functions represents a vertical shift of the parent function f(x) = |x|?

• f(x) = -|x|

• f(x) = (1/4)|x + 6|

• f(x) = 3|x| - 2

• f(x) = |x| + 9

• f(x) = |x - 5|

The vertex form of an absolute value function is written as: f(x) = a|x - h| + k, where (h, k) is the vertex, a is the slope on the right side and -a is the slope on the left side.

• f(x) = a|x - h| + k

• f(x) = a(x - h)^2 + k

• f(x) = a|x + h| - k

• f(x) = a(x + h)^2 - k