Use Equation A and describe the differences to show the change from

Question

f(x) = x to the equation A.
Equation A: f(x) = 3х - 4

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

Answer 1

To describe the differences between the function \( f(x) = x \) and Equation A, \( f(x) = 3x - 4 \), we can break down the changes in the slope and the y-intercept.

1. Slope Change:

   • The original function \( f(x) = x \) has a slope of 1.
   • The new function \( f(x) = 3x - 4 \) has a slope of 3.
   • This indicates 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 of 0 (it crosses the y-axis at the point (0,0)).
   • The new function \( f(x) = 3x - 4 \) has a y-intercept of -4 (it crosses the y-axis at the point (0, -4)).
   • This indicates that the graph of the function moves down the y-axis by 4 units.

Combining these two observations, the correct statement is:

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

So the correct choice is the first one: The slope increases by a factor of 3 and the graph of the function moves down the y-axis 4 units.