Final answer:
The function a(x) = 5f(x) – 5 results in the original graph of f(x) becoming steeper because of the multiplication by 5, and it shifts down by 5 units on the y-axis due to the subtraction of 5.
Step-by-step explanation:
Understanding the Transformation of f(x)
When we look at the function a(x) = 5f(x) – 5, we can interpret the transformation applied to the original function f(x). The multiplication by 5 indicates that the slope of the graph is increased by a factor of 5, which suggests that if f(x) had any slope originally, it is now steeper. This explains the change in steepness compared to f(x).
The subtraction by 5 indicates a vertical shift downwards by 5 units. This transformation is what moves the entire graph of the function down, which does not affect the slope but changes the y-intercept. Therefore, we consider this to be a shift down 5 units.
In conclusion, the correct answer choices would be that the transformation of f(x) into a(x) makes the graph steeper and shifts it down 5 units.