Problem 129 - College Algebra

Question

What must be done to a function's equation so that its graph is shifted vertically upward?

Step-by-Step Solution

Answer

To shift the graph of a function vertically upward, a positive constant needs to be added to the function's equation.

Step 1: Understanding Vertical Transformations

When a constant is added (or subtracted) to a function, it causes a shift in the graph of the function along the y-axis. This is known as vertical transformation. The magnitude and direction of the shift is determined by the value and sign of the constant.

Step 2: Application to the Function's Equation

To shift a function's graph upwards, a positive constant must be added to the function. Specifically, if \( f(x) \) is the original function, the transformed function \( g(x) \) would be \( g(x) = f(x) + c \), where \( c \) is a positive constant. The value of \( c \) determines how much the function's graph is shifted upward.