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

Question

to the equation A.

Equation A: f(x)=3x−4

Responses

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 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.

Answer 1

To analyze the change from the function $f(x)=x$ to the equation $f(x)=3x-4$, we can break down the transformations involving slope and vertical shifts.

1. Change in Slope:

   • The original function $f(x)=x$ has a slope of 1 (since it can be expressed as $f(x)=1x+0$).
   • In Equation A, $f(x)=3x-4$, the slope is 3.
   • Therefore, the slope increases from 1 to 3, which is an increase by a factor of 3.

2. Change in Vertical Position:

   • The original function $f(x)=x$ has a y-intercept of 0 (the graph intersects the y-axis at the point (0,0)).
   • In Equation A, the y-intercept is -4 (the graph intersects the y-axis at the point (0,-4)).
   • This means the entire graph of the function moves down the y-axis by 4 units.

Combining these observations, we can conclude that:

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.