The function that describes the given graph is:
f(x) = 3*cos(x) + x
Which function describes the graph?
Notice that in the description, we know that the graph intercepts the y-axis at (0, 6).
This means that f(0) = 6.
Now, just let's evaluate all the options in x = 0 and let's see if we can discard some of them.
- a) f(0) = 6*cos(0) = 6
- b) f(0) = 3*cos(0) + 3 = 6
- c) f(0) = 6*sin(0) = 0
- d) (0) = 3*sin(0) + 3 = 3
So. we can discard the two sine functions.
Now, we also know that the minimum value of our function is 0.
Notice that for the first option:
f(x) = 6*cos(x).
The maximum value is when cos(x) = 1, which gives 6, and the minimum value is when cos(x) = -1, which gives -6.
For the other option:
f(x) = 3*cos(x) + 3
The minimum is when cos(x) = -1, which gives:
3*-1 + 3 = -3 + 3 = 0
So we can conclude that this is the correct option.
f(x) = 3*cos(x) + x.
If you want to learn more about trigonometric functions, you can read:
https://brainly.com/question/8120556
