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 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 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.
The slope increases 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 analyze the differences between the functions \(f(x) = x\) and \(f(x) = 3x - 4\), we can look at the slope and the y-intercept of each equation.

1. The function \(f(x) = x\) has a slope of 1 and a y-intercept of 0.
2. The function \(f(x) = 3x - 4\) has a slope of 3 and a y-intercept of -4.

Now let's break down the changes:

- The slope **increases** from 1 to 3. This means the slope increases by a factor of 3 (because \(3 \div 1 = 3\)).
- The graph of the function moves **down the y-axis** from 0 to -4, which is a downward shift of 4 units.

Therefore, the correct option is:
**The slope increases by a factor of 3 and the graph of the function moves down the y-axis 4 units.**