Question

Functions f(x) and g(x) are shown below: f(x) g(x) f(x) = −4(x − 6)2 + 3 graph of cosine function which starts at 0 comma 2 and increases to the maximum at pi over 2 then decreases to the minimum at 2 pi where the cycle repeats Courtesy of Texas Instruments Using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.

Answer 1

Since f(x) is written in vertex form with a negtive vertical expansion factor, we know it opens downward and the maximum is at the vertex, 3.

Since we have a graph of g(x), we can read the maximum from the graph, 4.

We can determine which function has the largest maximum by noting that the largest maximum is 4 and that it corresponds to function g(x).