pre-calculus section 1-3b functions and their graphs
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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
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