Unit 1, Part 2
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Transcript of Unit 1, Part 2
Unit 1, Part 2
Families of Functions, Domain & Range, Shifting
Functions What is a function? What are the different ways to
represent a function?
Important questions for the unit…
• What is a function?• What is domain?• What is range?
FunctionA function is a mathematical “rule”
that for each “input” (x-value) there is one and only one “output” (y – value).
A function has a domain (input or x) and a range (output or y)
Examples of a Function
{ (2,3) (4,6) (7,8)(-1,2)(0,4)} 4
-2
1
8
-4
2
4
-2
1
8
-4
2
Non – Examples of a Function
{(1,2) (1,3) (1,4) (2,3)}
Vertical Line Test – if it passes through the graph more than once then it is NOT a function.
You Do: Is it a Function? Give the domain and range of each (whether it’s a function or not).
1.{(2,3) (2,4) (3,5) (4,1)}
2.{(1,2) (-1,3) (5,3) (-2,4)}
3. 4.
5.
0
-3
4
1
-5
9
Parent Functions
–F(x) = x–F(x) = x²–F(x) = x³ –F(x) = l x l–F(x) = √(x) –F(x) = 1
x
Shifting Functions
• On your graph paper, graph each parent function.• Graph the following functions (calc, table, however
you’d like).– F(x) = x +3– F(x) = x² + 3 and F(x) = (x + 3)²– F(x) = x³ -2 and F(x) = (x – 2)³ – F(x) = l x l – 4 and F(x) = l x – 4 l– F(x) = √(x) + 1 and F(x) = √(x + 1) – F(x) = 1 and F(x) = 1 - 2
x– 2 x
Shifting continued…
• Looking at the graphs, in small groups see if you can come up with a rule for how graphs are shifted.
Shifting again…
• Use your rule to graph these and describe how they are shifted.– F(x) = x -7– F(x) = (x + 4)² - 2 – F(x) = (x – 2)³ + 6– F(x) = l x – 5 l – 4 – F(x) = √(x + 10) + 3– F(x) = 1 + 3
x– 8
Piecewise Functions
• Give the domain and range of the following function.