Answer:
- maximum: 13
- minimum: 5
- period: π
Explanation:
You start by putting aside your fear and/or hatred of math. You acknowledge that you are fully capable of working these problems with no anxiety or doubt.
Start by looking at the equation. It is of the form ...
function name = function definition
and the function definition is of the form ...
(number)(trig function) + (number)
= 4·cos( ) + 9
It is important to note here that the function definition is basically a sum.
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The trig function involved here is the cosine (cos) function. That means its graph goes back and forth between -1 and +1. Its range of values is limited to numbers between these.
Since the two numbers noted in the function form above don't change, the maximum and minimum of the sum can be easily figured. The values of the cosine function are multiplied by 4, and 9 is added to the result of that.
The minimum will be 4·(-1) + 9 = 5.
The maximum will be 4·(+1) + 9 = 13.
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The period of the function has to do with the stuff inside parentheses of the cosine function. Here, that stuff is ...
(2x -π/2)
We want to find the change in x that will make the change in this expression be equal to 2π. We observe that x is multiplied by 2, so to make the value of that product change by 2π, we only need to change x by π. (You can basically ignore the "-π/2" when figuring the period.)
So, the period is π. On a graph, it is the horizontal distance between corresponding points, such as peaks. Here, the peaks are at x=π/4 and at x=5π/4. These values differ by (5-1)π/4 = 4π/4 = π. This is the period: π.