Problem 129 - Precalculus Essentials

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 a function's graph vertically upwards, a positive constant should be added to the function's equation.

Step 1: Concept understanding

In general, for any function f(x), if a constant c is added to that function, i.e., the new function becomes f(x) + c, it results in a vertical shift in the graph of the function. The direction (upward or downward) depends upon the value of c.

Step 2: Identifying the vertical upward shift

If the constant c is positive, the graph of the function f(x) + c shifts c units upwards from the initial position of the function f(x). Hence, to get a vertical upward shift, a positive constant must be added to the function's equation.