Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is .

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be the base formula, where is measured in sexagesimal degrees. This expression must be transformed by using the following data:

(Period)

(Minimum)

(Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of radians. In addition, the following considerations must be taken into account for transformations:

1) must be replaced by . (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

The new function is:

Given that , and , the outcome is:

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.