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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 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 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 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.
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1 answer

To compare the functions \( f(x) = x \) and \( f(x) = 3x - 4 \), we can analyze the changes in slope and vertical translation between the two equations.

  1. Slope:

    • For \( f(x) = x \), the slope is 1 (since it can be rewritten as \( f(x) = 1x + 0 \)).
    • In Equation A, \( f(x) = 3x - 4 \), the slope is 3.
    • This means the slope increases by a factor of 3 (from 1 to 3).

  2. Vertical Translation:

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

So, the correct response that summarizes these changes is:

The slope increases by a factor of 3 and the graph of the function moves down the y-axis 4 units.