Question

Given the parent function of f(x)=x³, 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

Answer 1

The change to the function f(x)=x³ when altered to f(x)−3 is a vertical shift downwards by 3 units (d. Shift down 3 units). This shift does not affect the horizontal position of the graph but moves it lower on the y-axis.

Step-by-step explanation:

When the function f(x)=x³ is changed to f(x)−3, this represents a vertical shift of the graph of the function downwards by 3 units. Therefore, the correct answer to what change will occur is d. Shift down 3 units.

The subtraction of a number from the entire function (outside of the cubic function itself) moves the graph vertically. Specifically:

• If a number is subtracted from the function (f(x) - number), the graph shifts down.
• If a number is added to the function (f(x) + number), the graph shifts up.

This is an example of vertical translation in function transformations.