We want to find the coefficients of a given function such that the graph of the function matches the given graph.
We will get:
a = -0.5
d = -3
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We start with the general function:
f(x) = a*cos(x) + d.
Let's analyze the graph
In the figure, we can see that the graph passes through the point (0, -3.5)
This means that our function evaluated in x = 0 is equal to -3.5, then we can write:
f(0) = a*cos(0) + d = -3.5
a + d = -3.5
We also can see that the distance between a peak and a through is 1 unit, and a, the amplitude, must be (in absolute value) half of that. Also note that when x = 0 we have a local minimum, while for the normal cosine we have a local maximum at x = 0, then a must be a negative number.
Then we have that:
a = - (1/2) = -0.5
Now that we know the value of a we can replace it in the other equation to get:
a + d = -3.5
-0.5 + d = -3.5
d = -3.5 + 0.5 = -3
Then the values of a and d are:
a = -0.5
d = -3
The function is:
f(x) = -0.5*cos(x) - 3
And the graph of this can be seen at the end of the answer, where it does not match exactly because the x-scale in the image is in units of pi, while in my graph is in integers.
If you want to learn more, you can read:
https://brainly.com/question/17954123
