Question

Given the parent function of f(x) = x^2, what change will occur when the function is changed to f(x) - 3?

A. Shift to the right 3 units.

B. Shift to the left 3 units.

C. Shift up 3 units.

D. Shift down 3 units.

You can choose the correct answer from these options.

Answer 1

Subtracting 3 from the function f(x) = x^2 results in a downward shift of the graph by 3 units, hence the answer is D. Shift down 3 units.

Step-by-step explanation:

When altering the parent function f(x) = x^2 to f(x) - 3, the graph of the function shifts vertically. The subtraction of 3 from the function value will translate the graph downward by 3 units. This is because the modification affects the output values of the function directly, changing each y-value. The correct answer to which change occurs when the function is changed to f(x) - 3 is D. Shift down 3 units.

When the function f(x) = x^2 is changed to f(x) - 3, it means that every y-value of the function will be shifted downward by 3 units. This corresponds to a shift downward 3 units from the original parent function.