Question

student activity sheet 3; exploring \generalizing transformations\ 9. reinforce the graph of the parent - function rule g(x), the solid line, has been transformed to create the graph of a new function rule af(x - h)+k, the dashed line. using the answer choices provided, fill in the blanks to complete true statements about the values a, h, and k. wider narrower a > 1 a is negative 0 < a < 1 |a| > 1 left right negative positive up down a: the transformed function graph is ______ than the original graph, so ____. h: the transformed function graph is shifted to the ____, so h is ____. k: the transformed function graph is shifted ____, so k is ______.

Explanation:

Step1: Analyze the value of a

The transformed graph is narrower than the original graph. When $|a|>1$, the graph of $y = af(x - h)+k$ is narrower than the graph of $y = f(x)$. So $|a|>1$.

Step2: Analyze the value of h

The transformed function graph is shifted to the left. For a horizontal shift of the function $y = f(x)$ to $y=f(x - h)$, a left - shift means $h<0$ (negative).

Step3: Analyze the value of k

The transformed function graph is shifted up. For a vertical shift of the function $y = f(x)$ to $y = f(x - h)+k$, an upward shift means $k>0$ (positive).

Answer:

a: narrower; $|a|>1$
h: left; negative
k: up; positive