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

Question

Equation A:  f(x)=3x−4

(1 point)
Responses

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 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 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 \( f(x) = 3x - 4 \):

1. Slope Change:

   • The slope of \( f(x) = x \) is 1.
   • The slope of \( f(x) = 3x - 4 \) is 3.
   • Therefore, the slope actually increases by a factor of 3 (from 1 to 3).

2. Y-intercept Change:

   • The y-intercept of \( f(x) = x \) is 0 (at the point (0,0)).
   • The y-intercept of \( f(x) = 3x - 4 \) is -4 (at the point (0,-4)).
   • Therefore, the graph of the function moves down the y-axis by 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.