Our Library of Elementary Functions is the starting point. The Elementary Functions are our basic building blocks. We use them to construct other, more complex, functions. And, many new functions can be created from these functions.

$\blacktriangleright$ Arithmetic: A new function can be created as the sum, difference, product, or quotient of two known functions.

$\blacktriangleright$ Piecewise: A new function can be created by gluing together pieces of other functions.

$\blacktriangleright$ Shifting: A function is essentially a collection of domain-range pairs.

• We can shift the domain numbers in the pairs to create a new function.
• We can shift the range numbers in the pairs to create a new function.

Learning Outcomes

In this section, students will

• examine the effects of shifting a domain.
• examine the effects of shifting a range.