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.
1 answer:
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).
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a.
In order to find the common ratio, we just need to divide a term by the term that comes before it.
So using the terms 20 and -5, we have:
b.
The recursive rule can be found with the formula:
Where an is the nth term and q is the ratio. So we have:
c.
The explicit rule can be written as:
Where an is the nth term, a1 is the first term and q is the ratio. So: