Question

Write a formula for the function g that results when the graph of the toolkit function f(x) = |x| is reflected over the y-axis and horizontally compressed by a factor of 1/7.

a) g(x) = |x| / 7
b) g(x) = -|7x|
c) g(x) = -|x| / 7
d) g(x) = |7x|

Answer 1

The formula for the function g(x) resulting from reflecting f(x) = |x| over the y-axis and horizontally compressing by a factor of 1/7 is g(x) = |7x|, which is option d.

Step-by-step explanation:

The question asks to find the formula for the function g(x) that results from reflecting the graph of the toolkit function f(x) = |x| over the y-axis and horizontally compressing it by a factor of 1/7. Reflection over the y-axis would replace x with -x, resulting in f(-x) = |−x|. However, reflecting over the y-axis does not change the graph of |x| because it is already symmetric about the y-axis. Therefore, the expression remains |x|. Next, compressing the graph horizontally by a factor of 1/7 means we multiply x by 7 within the absolute value, resulting in g(x) = |7x|. Thus, the correct formula is represented by option d) g(x) = |7x|.