Problem 130 - College Algebra

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 a function's graph to the right, subtract a positive constant from the x-values in the function's equation. This results in a horizontal shift to the right by the value of the constant.

Step 1: Understanding horizontal shifts

A horizontal shift is when the graph of a function is moved left or right. This is achieved by adding or subtracting a constant from the x-values in the function.

Step 2: Applying a shift to the right

To shift a graph to the right, a constant must be subtracted from the x-values in the function's equation. This results in the graph shifting to the right by the value of the constant. The general form for a horizontal shift to the right is \( f(x + h) \), where h is the constant, and f represents the function. If the function equation is \( y = f(x) \), after shifting to the right by h units, the function equation would be: \( y = f(x - h) \). If h > 0, the graph will shift to the right by h units.