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

Question

to the equation A.

Equation A: f(x)=3x−4

(1 point)
Responses

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.
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 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 up the y-axis 4 units.

Answer 1

To describe the changes from the function \( f(x) = x \) to Equation A, \( f(x) = 3x - 4 \), we analyze the components of the two equations.

1. Slope:

   • The original function \( f(x) = x \) has a slope of 1.
   • In Equation A, \( f(x) = 3x - 4 \), the slope is 3.
   • Therefore, the slope increases by a factor of 3.

2. Y-intercept:

   • The original function has a y-intercept of 0 (where the line crosses the y-axis).
   • In Equation A, the function has a y-intercept of -4.
   • This means the graph of the function moves downward along the y-axis by 4 units.

Given 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.