Problem 130 - Precalculus Essentials

Question

What must be done to a function's equation so that its graph is shifted horizontally to the right?

Step-by-Step Solution

Answer

To shift the graph of a function to the right, add a positive value inside the parentheses with the variable in the function's equation, e.g., \( f(x-h) \).

Step 1: Understand the effect of horizontal shifts

A horizontal shift, also known as a horizontal translation, moves the function's graph left or right. It doesn't change the shape or orientation of the graph. An increase in the input (x-value) corresponds to a shift to the right, while a decrease corresponds to a shift to the left.

Step 2: Identify the key part in function's equation responsible for horizontal shift

Horizontal shifts are implemented in the function's equation by adding or subtracting a value 'h' inside the parentheses with the variable, like this: \( f(x-h) \). If 'h' is positive, the graph shifts to the right. If 'h' is negative, the graph shifts to the left.

Step 3: Specify the condition for shifting the function's graph to the right

To shift the function's graph to the right, add a positive constant 'h' inside the parentheses with the variable in the function's equation. The new function will look like this: \( f(x-h) \).