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Finding Values and Domains, Average Rate of Change, and Odd/Even Functions

An even function is defined as f(x) = f(-x), and an odd function has -f(x) = f(-x).
The domain of a function is the set of input data that keeps the function defined.
Determine if the function f(x) = -2x^2 * absolute value(-6x) is even, odd, or neither.
Find the average rate of change for the function f(x) = 4/(x+3) between the values of 1 and x.

Solution Summary

This question has multiple questions and multiple parts. The first question has four parts that show how to take a given function and evaluate it for a specific x-value, including the quantity "x+h" used in the definition of a derivative.

The second question looks at finding the domain of a function. A specific example is given showing how the insertion of parentheses can change the value of the domain. This particular function uses radicals.

The third question has two parts and looks at combining f(x) and g(x) through multiplication and division. An evaluation of the domain is made in each case. Also, it is instructive to see how the similarities and differences in the domain.

The fourth question discusses the requirements for a function to be even or odd and gives a specific example This example includes absolute value.

The fifth question demonstrates how to reflect a function about the x-axis.

Finally, the sixth function finds the average rate of change for a given function between two points.