Pre-CalculusSection 1-3B

Functions and Their Graphs

Graphing a Piecewise - Defined Function

- Graph by hand (you can use the graphing

calculator to guide you)

- Use the domain portions to split the graph

into parts (draw dashed vertical lines)

Need to remember the following graphs

- line: y = mx + b

- parabola: y = x2

- absolute value: shape

- square root: half parabola

Graph the Piecewise - Defined Function

Test for Even and Odd Functions

A function is even if, for each x in the domain of f, f (-x) = f (x)

So …

1. you replace all of the x’s with (-x)’s

2. evaluate the expression

3. if you “end up” with the original function

the function is even

A function is odd if, for each x in the domain of f, f (-x) = - f (x)

So …

1. you replace all of the x’s with (-x)’s

2. evaluate the expression

3. if you “end up” with the opposite of the

original function the function is odd

( you normally have to factor a -1 out of the

expression)

Determine if the function is even, odd, or neither.

4. g(x) = x3 - x

Determine if the function is even, odd, or neither.

5. h(x) = x2 + 1

Determine if the function is even, odd, or neither.

6. f(x) = x3 - 1

Determine even or oddness graphically.

Even Functions - are symmetric with respect to the y-axis

(-x, y) (x, y)

Odd Functions - are symmetric with respect to the origin

(-x, -y) (x, y)

Use your graphing calculator to determine if the function is even, odd, or neither.

7. f(x) = 3x - 2

Use your graphing calculator to determine if the function is ever, odd, or neither.

8. g(x) = x2 - 4

Use your graphing calculator to determine if the function is ever, odd, or neither.

9. h(x) = │x + 2│

Homework:

Page 39 - 41

44 - 50 Evens

60 - 82 Evens

95 - 100 All