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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 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 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 up the y-axis 4 units.

1 answer

To compare the function \( f(x) = x \) and the given Equation A, \( f(x) = 3x - 4 \), we can break it down into two main components: the slope and the y-intercept.

  1. Slope:

    • In \( f(x) = x \), the slope is 1 (or \( 1x + 0 \)).
    • In Equation A, \( f(x) = 3x - 4 \), the slope is 3.
    • Therefore, the slope increases by a factor of 3 (from 1 to 3).

  2. Y-intercept:

    • The y-intercept of \( f(x) = x \) is 0.
    • The y-intercept of Equation A is -4.
    • This means the graph of the function moves down the y-axis 4 units (from 0 to -4).

Combining these observations, we can conclude:

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.