Characteristics of Polynomials: Domain, Range, & Intercepts Daily Questions……. What is interval notation? 3. What is the domain & range of a function? 4. How do I find the intercepts of a functions graphically and algebraically?

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 Range all the x-values Read the graph from left to right all the y-values Read the graph from bottom to top

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

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

With polynomials…. The DOMAIN is always All Reals, , The RANGE will be: All Reals, , Lower Boundary to infinity, Negative infinity to Upper Boundary,

Zeros/x-intercepts/Solutions/Roots Where the graph crosses the x-axis What’s a zero? Zeros/x-intercepts/Solutions/Roots Where the graph crosses the x-axis

Where the graph crosses the x-axis. Also called zeros. Analyze the Graph of a Function x-intercepts Where the graph crosses the x-axis. Also called zeros. Zeros: 1, 5

X-Intercepts: (-2, 0) (-2, 0) (3,0) Zeros, Roots: x = -2, -2, 3

X-Intercepts: (-1,0)(1,0)(2,0) Zeros, Roots x = -1, 1, 2

y-intercepts Where the graph crosses the y-axis

y-Intercept: (0,-12)

y-Intercept: (0,2)

Y- int: (0, -1) # of zeros: 4 Y- int: (0, 15) # of zeros: 2 Find the y-intercepts & number of zeros: a) b) Y- int: (0, -1) # of zeros: 4 Y- int: (0, 15) # of zeros: 2

All reals All reals (-2,0)(-2,0)(1,0) (0, -4) Find the following Domain: Range: 3. x-intercepts: 4. y-intercepts: All reals All reals (-2,0)(-2,0)(1,0) (0, -4)

All reals [-4, ∞) -2, 2 (0, -4) Find the following Domain: Range: 3. Zeros: 4. y-intercepts: All reals [-4, ∞) -2, 2 (0, -4)

Increasing Decreasing Constant This is a piecewise function

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

Increasing and decreasing are stated in terms of domain Ex. 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: all of the lowest points Relative Maximum: all of the highest points

Absolute Minimum & Maximum Absolute Minimum: the lowest point Absolute Maximum: the highest point

Relative maximum Relative minimum

All reals All reals -2, -2, 1 (0, -4) none max: (-2, 0) min: (0, -4) 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, -2, 1 (0, -4) none max: (-2, 0) min: (0, -4)

All reals [-4, ∞) -2, 2 (0, -4) min: (0, -4) min: (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 [-4, ∞) -2, 2 (0, -4) min: (0, -4) min: (0, -4) (0, ∞) (-∞, 0)