Problem 59 - 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 should be added to the function's equation.

Step 1: Understanding Shifting of Function Graphs

Before we proceed to the operation, let's understand how shifting occurs in the graphs of functions. A vertical shift up or down happens when a constant is added or subtracted from a function.

Step 2: Upwards Shift Operation

For an upward shift, we add a positive constant to the function. Hence, if we have a function denoted by \(f(x)\), to shift its graph upwards by a units, we transform it into \(f(x) + a\).