Question

Use Equation A and describe the differences to show the change from
f(x) = x to the equation A.
Equation A: f(x) = 3х - 4

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

Answer 1

To describe the differences between the function \( f(x) = x \) and Equation A, \( f(x) = 3x - 4 \), we can break down the changes in the slope and the y-intercept.

1. **Slope Change**:
- The original function \( f(x) = x \) has a slope of 1.
- The new function \( f(x) = 3x - 4 \) has a slope of 3.
- This indicates that the slope increases by a factor of 3 (from 1 to 3).

2. **Y-Intercept Change**:
- The original function \( f(x) = x \) has a y-intercept of 0 (it crosses the y-axis at the point (0,0)).
- The new function \( f(x) = 3x - 4 \) has a y-intercept of -4 (it crosses the y-axis at the point (0, -4)).
- This indicates that the graph of the function moves down the y-axis by 4 units.

Combining these two observations, the correct statement is:

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

So the correct choice is the first one:
**The slope increases by a factor of 3 and the graph of the function moves down the y-axis 4 units.**