Question

1. let $f(x) = x$ and $g(x) = 6x - 1$. complete the following statements to compare the graph of $g(x)$ to the graph of $f(x)$. the graph of $g(x)$ is shifted up down from the graph of $f(x)$.

Explanation:

Step1: Recall Vertical Shift Rule

For a linear function \( y = mx + b \), the value of \( b \) determines vertical shift. If \( b>0 \), shift up \( |b| \) units; if \( b<0 \), shift down \( |b| \) units.

Step2: Analyze \( f(x) \) and \( g(x) \)

\( f(x)=x \) can be written as \( f(x)=1x + 0 \), \( g(x)=6x - 1 \) has \( b=-1 \). Since \( b=-1<0 \), the graph of \( g(x) \) is shifted down by \( 1 \) unit from \( f(x) \).

Answer:

down