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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 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.

1 answer

To compare the two equations \( f(x) = x \) and \( f(x) = 3x - 4 \), we analyze the changes in slope and y-intercept.

  1. Slope:

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

  2. Y-Intercept:

    • The original function \( f(x) = x \) has a y-intercept at (0, 0).
    • The new function \( f(x) = 3x - 4 \) has a y-intercept at (0, -4).
    • This indicates that the graph of the function moves down the y-axis by 4 units.

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.