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

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

Answer 1

To understand the differences between the function \( f(x)=x \) and Equation A \( f(x)=3x−4 \), we can analyze the changes in the slope and the vertical position (y-intercept) of the graph.

1. Slope Change:

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

2. Y-Intercept Change:

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

Based on these changes, we can conclude that:

• The slope increases by a factor of 3 (from 1 to 3).
• The graph of the function moves down the y-axis by 4 units (from y=0 to y=-4).

Therefore, the correct response from the options given is:

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