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). the graph of g(x) is steeper less steep than the graph of f(x).

Explanation:

Step1: Analyze Vertical Shift

For linear functions \( y = mx + b \), the \( b \)-value (y - intercept) determines vertical shift. \( f(x)=x \) has \( b = 0 \), \( g(x)=6x - 1 \) has \( b=-1 \). A negative \( b \) means shifting down (since \( -1<0 \)).

Step2: Analyze Slope (Steepness)

Slope \( m \) determines steepness. \( |m| \)越大, steeper the line. \( f(x) \) has \( m = 1 \), \( g(x) \) has \( m = 6 \). Since \( |6|>|1| \), \( g(x) \) is steeper.

Answer:

The graph of \( g(x) \) is shifted \(\boldsymbol{\text{down}}\) from the graph of \( f(x) \).
The graph of \( g(x) \) is \(\boldsymbol{\text{steeper}}\) than the graph of \( f(x) \).