Question

1. let $f(x) = x$ and $g(x) = \frac{6}{5}x + 5$. which two of the following statements are true? select both correct options. the graph of $g(x)$ is shifted down from the graph of $f(x)$. the graph of $g(x)$ is shifted up from the graph of $f(x)$. the graph of $g(x)$ is steeper than the graph of $f(x)$. the graph of $g(x)$ is less steep than the graph of $f(x)$. yay! first question of the day. 20

Explanation:

Step1: Analyze vertical shift

The function \( f(x) = x \) (slope \( m_1 = 1 \), y - intercept \( b_1 = 0 \)) and \( g(x)=\frac{6}{5}x + 5 \) (slope \( m_2=\frac{6}{5} \), y - intercept \( b_2 = 5 \)). Since \( b_2=5>b_1 = 0 \), the graph of \( g(x) \) is shifted up from \( f(x) \).

Step2: Analyze steepness (slope comparison)

The slope of \( f(x) \) is \( m_1 = 1=\frac{5}{5} \), and the slope of \( g(x) \) is \( m_2=\frac{6}{5} \). Since \( \frac{6}{5}> \frac{5}{5}=1 \), the slope of \( g(x) \) is greater than the slope of \( f(x) \). A larger slope means a steeper line, so the graph of \( g(x) \) is steeper than the graph of \( f(x) \).

Answer:

B. The graph of \( g(x) \) is shifted up from the graph of \( f(x) \)
C. The graph of \( g(x) \) is steeper than the graph of \( f(x) \)