Question

Suppose f(x) = 3x + 5. Describe how the graph of each function compares to f. Remember, determine if it affects the input or output.

a. h(x) = f(x) - 7
A. It affects the input
B. It affects the output
C. It affects both the input and output
D. It affects neither the input nor the output

Answer 1

The function h(x) = f(x) - 7 differs from f(x) = 3x + 5 by shifting the graph of f(x) downwards by 7 units on the y-axis, which means it alters the output.

Step-by-step explanation:

When comparing the function h(x) = f(x) - 7 to the original function f(x) = 3x + 5, we need to determine how this transformation affects the graph of the function. Subtracting 7 from the function f(x) shifts the entire graph of f(x) downwards by 7 units on the y-axis. This is because the subtraction of 7 affects the output (y-value) of the function, not the input (x-value).

Therefore, the correct answer is:

• B. It affects the output