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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 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.
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 up the y-axis 4 units.

1 answer

To compare the functions \( f(x) = x \) and Equation A \( f(x) = 3x - 4 \), we should analyze how the coefficients of \( x \) and the constant term change the graph of the function.

  1. Slope Change:

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

  2. Y-Intercept Change:

    • The original function \( f(x) = x \) has a y-intercept at \( (0, 0) \).
    • The y-intercept of Equation A can be found by setting \( x = 0 \): \[ f(0) = 3(0) - 4 = -4 \]
    • This means the graph of the function shifts down 4 units on the y-axis.

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.