Question

Question
Use Equation A and describe the differences to show the change from f(x)=x
to the equation A.

Equation A: f(x)=3x−4

(1 point)
Responses

The slope decreases by a factor of 3 and the graph of the function moves up the y-axis 4 units.

The slope increases by a factor of 3 and the graph of the function moves up the y-axis 4 units.

The slope decreases by a factor of 3 and the graph of the function moves down the y-axis 4 units.

The slope increases by a factor of 3 and the graph of the function moves down the y-axis 4 units.

Answer 1

To compare the function \( f(x) = x \) to Equation A \( f(x) = 3x - 4 \), we need to examine the changes in slope and y-intercept.

1. **Slope**:
- The slope of \( f(x) = x \) is \( 1 \).
- The slope of \( f(x) = 3x - 4 \) is \( 3 \).
- Thus, the slope **increases by a factor of** \( 3 \) (from \( 1 \) to \( 3 \)).

2. **Y-Intercept**:
- The y-intercept of \( f(x) = x \) is \( 0 \).
- The y-intercept of \( f(x) = 3x - 4 \) is \( -4 \).
- Therefore, the graph of the function **moves down the y-axis** \( 4 \) units (from \( 0 \) to \( -4 \)).

Based on this analysis, the correct response is:

**The slope increases by a factor of 3 and the graph of the function moves down the y-axis 4 units.**