Question

1. reinforce the graph of the parent function rule f(x) (the solid blue line) has been transformed to create the graph of a new function rule af(x - h)+k (the dashed blue line). using the answer choices provided, fill in the blanks to complete true statements about the values of 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

If \(|a|> 1\), the graph of \(y = af(x)\) is narrower than the graph of \(y = f(x)\). If \(0 < a<1\), the graph of \(y=af(x)\) is wider than the graph of \(y = f(x)\). Looking at the graph, the transformed - function graph is wider than the original graph, so \(0 < a<1\).

Step2: Analyze the value of h

The transformation \(y = f(x - h)\) shifts the graph of \(y = f(x)\) to the right if \(h>0\) and to the left if \(h < 0\). The transformed - function graph is shifted to the right, so \(h\) is positive.

Step3: Analyze the value of k

The transformation \(y=f(x)+k\) shifts the graph of \(y = f(x)\) up if \(k>0\) and down if \(k < 0\). The transformed - function graph is shifted down, so \(k\) is negative.

Answer:

a: wider; \(0 < a<1\)
h: right; positive
k: down; negative