F(x) = 2cos(x) and g(x) = 3 sin (x+pi). using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.

The maximum value, generally, for either cosine or sine function is 1. If the function is multiplied by some co-efficient, then that would determine its maximum value. In the question, the given equations are:

F(x) = 2cos(x) --- (1)
g(x) = 3 sin (x+pi) --- (2)

For equation (1), the function would have the maximum value when x = 0 or x = 2π. In those cases, the maximum value for F(x) would be 2.
For equation (2), the function would have the maximum value when x = 3π/2 or x = -π/2. In those cases, the maximum value for g(x) would be 3.

Hence, the function g(x) has the largest maximum y value.

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the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.