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 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 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 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.
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Answer 1

To analyze the changes from the function \( f(x) = x \) to Equation A \( f(x) = 3x - 4 \), we can break it down into two components: the slope and the y-intercept.

1. Slope Change:

   • The original function \( f(x) = x \) has a slope of 1.
   • In Equation A, the slope is 3 (the coefficient of \( x \)).
   • This means that 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).
   • In Equation A, when \( x = 0 \), \( f(0) = 3(0) - 4 = -4 \).
   • This indicates that the graph of the function moves down the y-axis by 4 units.

Putting it all together, we can conclude:

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

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