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# Graph to function: Find a trigonometric function ISBN: 9780321570567 2

## Solution for problem 29RE Chapter 1

Calculus: Early Transcendentals | 1st Edition

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Problem 29RE

Graph to function: Find a trigonometric func?tion ? represented by the graph in the figure.

Step-by-Step Solution:

Step-by-step solution Step 1 We need to find a trigonometric function f that satisfies the given graph. Step 2 We can observe from the graph that it is just an inverted cosine function. Thus, we assume that the function f is a cosine function. Next, we use the general cosine function f(t) = Acos B(tC) +D  where A : amplitude is |A|, B : period is 2, |B| C : phase shift is C, D : vertical shift is D. Step 3 Solving for A: We can observe from the graph that the function has a minimum value of -1 at x = 0 and a maximum value of 3 at x = . With t2ese, we can now get a value for A. maxmin Amplitude = 2 Amplitude = 3(21) = 2 Amplitude = 2 A =2 (inverted) Step 4 Solving for D: The vertical shift D is defined as: D = min_value+amplitude Hence, we got: D =1+2 D = 1

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##### ISBN: 9780321570567

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