Domain & Range (3.1)
Functions
(3.1)
(3.1)
Function Notation (3.2)
Transformations
(3.3)
(3.3)
100
Identify the domain and range.
{(4,1), (2,3), (4,0), (5,3)}
Domain:
{2,4,5}
Range:
{0,1,3}
100
Determine if the relation is a function. If it is, determine if it is one-to-one.
It is a function since each input has exactly one output.
It is one-to-one since each output has exactly one input.
100
Given the function, f(x)=2x-1 evaluate for x=4 .
f(x)=2(x)-1
f(4)=2(4)-1
f(4)=8-1
f(4)=7
100
Identify the type of transformation from the original graph.
original: f(x)=2x+1
transformed: g(x)=(2x+1)-4
the graph moves down 4
200
Identify the domain and range.
Domain: {-5,-1,0,2,4}
Range: {-5,-2, 0, 2, 3}
200
Determine if the relation is a function. If it is, determine if it is one-to-one.
{(4,1), (2,3), (4,0), (5,3)}
Not a function, the input 4 has two outputs 1 & 0.
200
Given the function, f(x)=-3x-8 find f(-2).
f(x)=-3x-8
f(-2)=-3(-2)-8
f(-2)=6-8
f(-2)=-2
200
Identify the type of transformation from the original graph.
original: f(x)=2x+1
transformed: g(x)=2(x+3)+1
the graph moves left 3
300
Identify the domain and range of the function.
Domain: {-3, -2, 1, 2, 5}
Range: {-5,0,1,4}
300
Determine if the function would have a discrete or continuous domain. Then find the domain.
A person drinks n ounces of a 20-ounce bottle of a sports drink.
This is continuous as the person will drink any amount of the sports drink up to the full 20 ounces. They could drink 1/4 oz., 0.0005 oz., 15 oz., etc.
D: 0<=x<=20
300
Given the function f(x)=2x-3, find x if f(x)=9.
f(x)=2x-3
9=2x-3
12=2x
6=x
x=6
300
Identify the transformation of the graph from f(x) to g(x).
the graph moves down 5
400
Identify the domain and range of the function.
Domain: -4<=x<=3
Range: -2<=y<=4
400
Determine if the relation is a function. If it is, determine if it is one-to-one.
{(5,2), (8,3), (7,3), (6,1)}
This is a function since each input has exactly one output.
This is not one-to-one since the output 3 has two inputs, 8 & 7.
400
A hotel charges $40 per hour to rent a computer plus a $65 security deposit. Write a function, in function notation, to model the cost of renting a computer.
f(x)=mx+b
m=40 ("40 PER hour")
b=65 ("starting fee")
f(x)=40x+65
400
Identify the type of transformation from the original graph.
original: f(x)=2x+1
transformed: g(x)=4(2x+1)
the graph is vertically stretched by 4
500
Identify the domain and range.
Domain: -4<=x<3
Range: -5<y<5
500
Determine if the relation is a function. If so, determine if it is one-to-one.
This is not a function, since the inputs have more than one output. For example, the input 0 has two outputs, 0 and 3.
500
Write an equation, in function notation, for the table below showing Melissa's earnings for her graphic design business.
f(x)=mx+b
m=(335-185)/(4-2)=150/2=75
f(x)=75x+b
185=75(2)+b
185=150+b
b=35
f(x)=7x+35
500
Identify the type of transformation from the original graph.
original: f(x)=2x+1
transformed: g(x)=2(4x)+1
the graph is horizontally compressed by 1/4