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

Question

𝑓
(
𝑥
)
=
𝑥
to the equation A.

Equation A: f(x)=3x−4
𝑓
(
𝑥
)
=
3
𝑥
−
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 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.
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 down the y-axis 4 units.

Answer 1

To compare the functions \( f(x) = x \) and \( f(x) = 3x - 4 \):

1. Slope Comparison:

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

2. Y-intercept Comparison:

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

Putting this together, 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.