Question

Let g(x) be the indicated transformation of f(x) = |2x| − 5. Compress the graph of f(x) = |2x| − 5 horizontally by a factor of 1/4 and reflect it across the x-axis. Identify the rule and graph of g(x).

Answer 1

Answer: g(x) = −|8x| + 5

The vertex is (0,5) and points down like an upside down V because it is reflected.

Explanation:

f(x) = |2x| − 5

For a horizontal compression use f ((1/b)x) where b < 1. To compress the graph horizontally by a factor of 1/4 substitute 1/4 for b in f ((1/b)x).

Therefore g(x) = f(4x) = |8x| − 5

To reflect the graph across the x-axis multiply the entire function by −1.

g(x) = −f(4x) = −|8x| + 5