See You at the Range
Am I a Function?
Better Take Not(ations)
Transformers
C's Get Degrees
100
Define Domain and Range.
Domain: all possible x values
Range: all possible y values
100
Describe two ways to determine a relation is a function.
Vertical line test
Every x has its own y
We know the relation is linear or quadratic (not a vertical line)
100
Given f(x) = 2x + 1, evaluate f(0).
f(0) = 2(0) + 1 = 1
100
Describe the transformations to f(x) = -x2
Vertical flip or reflection.
100
Is the following function linear, quadratic, or neither and how do you know?
f(x) = 3x +1
Linear because it is degree 1.
200
State the domain: {(0,-2), (1,-3),(2,-2),(3,4),(4,-3)}
Domain: {0, 1, 2, 3, 4}
200
Am I a function? How do you know?
No, the input of 2 has two different outputs.
200
Given h(t) = -3t2 + 100, evaluate h(4).
h(3) = -3(4)2 + 100
= -3(16) +100
= -48 + 100
= 52
200
Describe the transformations to f(x) = (x - 3)2 + 1
Horizontal shift right 3
Vertical shift up 1
200
Is the following function linear, quadratic, or neither and how do you know?
Neither, the 1st and 2nd differences are not the same. It is exponential.
300
State the range using the graph:
Range: {yER|y≥1}
300
Am I a function? How do you know?
Yes, it passes the vertical line test.
300
Given the table of values, evaluate f(-3).
f(-3) = -1
300
Describe the transformations to f(x) = 2x2 - 4
Vertical stretch by a factor of 2
Vertical shift down by 4
300
Is the following function linear, quadratic, or neither and how do you know?
{ (1 , 1), (2 , 4), (3 , 9), (4 , 16), (5 , 25)}
This relation is neither linear nor quadratic. First nor second differences are the same.
400
A ball is thrown off a roof from a height of 14 ft and lands 8 seconds later. State the domain using the graph.
Domain: {xER|0≤x≤8}
400
Am I a function? How do you know?
{(0,2), (-1,0), (2,3), (3,-2), (-1, 3)}
No, when x is -1 there are two possible y values.
400
Given the graph, evaluate f(x) = 7.
f(x) = 7 when x = 0 and x = 6
400
Describe the transformations to f(x) = -(x+2)2
Vertical flip or reflection
Horizontal shift left 2
400
The cost of a banquet is $550 for the room rental, plus $18 for each person served.
Is this relation linear, quadratic, or neither and how do you know?
The relationship is linear. There is a flat fee plus a rate of change.
500
State the range of the following function:
Range: {yER|y≤5}
500
Am I a function? If so, what type of function?
Yes, but it is neither a linear nor quadratic function.
500
Given f(x) = 3x2 + 2x – 5 and
h(x) = {(0,1), (2,3), (4,9), (5,0)},
evaluate f(1) – h(4).
f(1) = 3(1)2 + 2(1) – 5
= 3(1) + 2 – 5
= 3 + 2 – 5
= 0
h(4) = 9
f(1) – h(4) = 0 – 9 = -9
500
Describe the transformations to f(x) = -0.5x2 - 1
Vertical flip or reflection
Vertical compression by a factor of 0.5
Vertical shift down by 1
500
Using the degree, state whether the function is linear, quadratic, or neither:
g(x) = x2 – (x + 1)(x – 3)
g(x) = x2 – (x + 1)(x – 3)
= x2 – (x2 – 3x + 1x – 3)
= x2 – x2 + 3x - 1x + 3
= 2x + 3
Degree one; linear