Question

Section 3.03 on the OLS

Parent function is f(x) = |x|

Transformation Function g(x) = a|x – h| + k
Parent function is…
translated k units vertically
translated h unit horizontally (watch the sign)
vertex is at (h, k)
opens downward if a is negative
graph becomes wider if 0 < |a| < 1 or narrower if |a| > 1


1. Let g(x) be the indicated transformation of f(x) = |x|. Write the function rule for g(x) to describe the graph with a vertical shift for 5 units down.

Answer 1

2. Let g(x) be the indicated transformation of f(x) = |x|. Write the function rule for g(x) to describe the graph with a horizontal shift 3 units to the right.

Answer 2

3. Identify the vertex for f(x) = |x| + 2

Answer 3

4. Identify the vertex for g(x) = |x + 3| - 4

Answer 4

5. Translate f(x) = |x| so that the vertex is at the given point (3, -5). Write the new function as g(x).