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

Question

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

Answer 1

To analyze the change from the equation \( f(x) = x \) to the equation \( A: f(x) = 3x - 4 \), we can break down the transformations step by step.

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.
   • The slope has increased by a factor of 3 (from 1 to 3).

2. Y-Intercept Change:

   • The original function \( f(x) = x \) intercepts the y-axis at (0, 0).
   • The new function \( f(x) = 3x - 4 \) intercepts the y-axis at (0, -4).
   • This represents a vertical shift downwards by 4 units.

Combining these observations:

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

Based on this analysis, the correct option is:

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