Let’s Review Functions Daily Questions……. 1. What is interval notation? 2. What is the domain & range of a function? 3. When is a function increasing, decreasing, & constant? 4. Where are the max & min of a function?

How do we write in interval notation? x < 2…. when you want include use a bracket [ when you want to exclude use a parenthesis ( Let’s draw a number line first….

Draw a number line first…. Let’s do another type…. Draw a number line first….

Domain and Range Remember that domain is all the x-values (the input). Remember that range is all the y-values (the output).

What is the domain of f(x)? Ex. 1 (2,4) (-1,-5) (4,0) y = f(x) Domain

What is the range of f(x)? (2,4) (-1,-5) (4,0) y = f(x) Range

Determine the domain and range….

Increasing Decreasing Constant This is a piecewise function

Increasing and decreasing are stated in terms of domain Ex. 4b (-, -1) (-1, 1) (1, ) increasing decreasing increasing (-1,2) (1,-2)

Increasing and decreasing are stated in terms of domain Ex. 4c Increasing and decreasing are stated in terms of domain (-, 0) (0, 2) (2, ) constant increasing decreasing (0, 1) (2, 1)

Determine the intervals over which the function is increasing and decreasing…

Relative Minimum & Maximum Values (direction change) Relative minimum: lowest point in its relative area. Relative maximum: highest point in its relative area.

Relative maximum Relative minimum

All reals All reals (-2, 0) (1, 0) (0, -4) none (-2, 0) (-4, 0) Find the following Domain: Range: 3. Zeros: 4. y-intercepts: 5. Absolute Max/Min: 6. Relative Max/Min: 7. Increasing: 8. Decreasing: All reals All reals (-2, 0) (1, 0) (0, -4) none (-2, 0) (-4, 0)