Question

question 26 of 40
suppose that ( g(x)=f(x)-2 ). which statement best compares the graph of ( g(x) ) with the graph of ( f(x) )?
a. the graph of ( g(x) ) is shifted 2 units to the left.
b. the graph of ( g(x) ) is vertically stretched by a factor of 2.
c. the graph of ( g(x) ) is shifted 2 units down.
d. the graph of ( g(x) ) is shifted 2 units up.

Explanation:

Step1: Recall function transformation rules

For a function \(y = f(x)+k\), if \(k>0\), the graph is shifted \(k\) units up; if \(k < 0\), the graph is shifted \(|k|\) units down.

Step2: Analyze \(g(x)=f(x)-2\)

Here \(k=- 2\). According to the rule \(y = f(x)+k\), when \(k=-2\), the graph of \(y = f(x)\) is shifted \(2\) units down to get the graph of \(y=f(x)-2\).

Answer:

C. The graph of \(g(x)\) is shifted 2 units down.