Order of Operations - this tells us the order that we operate on numbers. This could be operating on a single number (e.g., $3^2$, where “squared” is operating on the number $3$) or between two numbers (e.g., $3*2$, where “multiplying” is operating on the numbers $3$ and $2$). But we don’t have to just operate on numbers! In fact, we’ve been operating on functions since Module 4 - Quadratic Functions. When we thought about how to graph a quadratic function, we could think about the parent function, $x^2$, and think about how the vertex is shifted and if the graph should be flipped (based on the leading coefficient). Shifting and flipping a function are ways we can operate on a function - we take a function and change it in a prescribed way. This Module will work through other ways we can operate on functions: adding/subtracting/multiplying/dividing, composing, and inverting.

The objectives for this Module are:

(a)

Identify the domain after operating $(+, -, \text {x}, \div )$ on functions.

(b)

Evaluate the composition of two functions.

(c)

Determine whether a function is 1-1.

(d)

Find the inverse of a function, if it exists.