Question

Identify the maximum values of the function y=8cos x in the interval [-2pi,2pi]. Use your understanding of transformations, not your graphing calculator

Answer 1

8

Explanation

to solve this we can start from the pattern function and check the transformation(s) made,so

Step 1

a) given the patter function

$y=cosx$

we know that the maximum values of the function cos x are:

Maximum value of sin A is 1 when A = 90 degrees

som the maximum value for the pattern function cos x is 1

Step 2

now, let's check the transformation

we have the function

$\begin{gathered} y=8cosx \\ y=8*cos\text{ x} \\ \end{gathered}$

so, the pattern function was multiplied by 8, when you multiply f(x) by a constant, a, the graph of f(x) is stretched vertically. The x-intercepts remain fixed because the y-value of these points is 0, which doesn't change when you multiply it by a constant,Multiplying the sine or cosine function by a constant (positive or negative) changes the maximum height and depth of its graph. so

$\begin{gathered} y=8*cosx \\ 8\text{ is the constant} \end{gathered}$

so, the maximum will be 8 times the maximum of the patter function

$\begin{gathered} maximum=constatn*maximim_1 \\ maximum=8*1 \\ maximum=8 \end{gathered}$

therefore, the answer is

8

I hope this helps you