Question

determine the effects on the graph of the parent function f(x)=x for the g(x)=9f(x) function. graph both functions on the same coordinate grid

determine the effects on the graph of the parent function f(x)=x for the g(x)=9f(x) function.

a. the graph becomes less steep.

b. the graph becomes steeper.

Explanation:

Step1: Recall function transformation

For a linear function \( f(x) = mx + b \), the slope is \( m \). The parent function \( f(x) = x \) has a slope \( m_1 = 1 \). The function \( g(x)=9f(x)=9x \) has a slope \( m_2 = 9 \).

Step2: Analyze slope effect on steepness

A larger absolute value of the slope means the graph is steeper. Since \( |9| > |1| \), the graph of \( g(x) \) is steeper than \( f(x) \).

Answer:

B. The graph becomes steeper.