Are You Having Fun(ction)?
Am I a function?
What's my function?
Key Features of Graphs
Domain & Range
Abs Value
The "Real" world
100
This word is used to describe the set of all inputs for a function.
What is the domain?
100
What is No, not a function? It does not pass the vertical line test.
100
f(-3) if f(x) = 2x +1
What it -5 ?
100
When is the function negative?
-5<x<-3.4, 5.7<x<=6
-3<=y<=6
100
Find the DOMAIN:
{(-2, 4), (3, 2), (2, 10)}
What is {-2, 3, 2}?
100
Describe the transformation from the parent function to the function below:
g(x) = -1/2 abs(x-9) + 2
A horizontal translation of 9 to the right, a vertical shrink by a factor of 1/2, a reflection over the x-axis, and a vertical translation of 2 up.
100
Sahara already knows 4 dance moves. She decides to take dance lessons to learn more new moves. The instructor tells her that she can learn two new moves each week.
Which functional equation can be used to find the number of dance moves (d) that Sahara knows after w weeks of lessons?
Choose:
d = 2w + 4
d = 4w + 2
d = 2w + 10
d = 2w - 4
d=2w+4
200
This word is used to describe the set of all outputs of a function.
What is the range?
200
What is Yes?
200
Let f(x) = x2 + x + 1; find f(-5).
What is 21?
200
Is shaded region increasing or decreasing? When is it the function increasing?
Decreasing; 3<x<6
200
Find RANGE:
y>=-1 [-1, infinity)
200
Compare the two functions below with three items:
f(x) = abs(x+1)-4 and g(x) = -abs(x-2)-4
Answers may vary:
one opens up and the other opens down
one has a vertex at (-1,-4) and the other at (2,-4)
one has a range of y>=-4 and the other y<=-4
200
Camille already knows 2 dance moves. She decides to take dance lessons to learn more new moves. The instructor tells her that she can learn three new moves each week.
How many weeks of dance lessons will it take for Camille to know a total of 11 dance moves?
3 weeks
300
What type of domain would be seen as a line on a graph instead of just individual points?
Continuous domain.
300
The mapping diagram shows a function or not.
What is No, not a function?
300
Based on the graph of the function, what is f(4)?
f(4) = -2
300
When is the function increasing?
-4<x<-2
300
Find DOMAIN:
all real numbers
(neg infinity, pos infinity)
300
f(x)=abs(x-2)
g(x)=-3abs(x-4)+3
Horizontal translation 2 to the right, vertical stretch by a factor of 3, reflection over the x, and a vertical translation 3 up.
300
Avril rode her bike 1 mile in 15 minutes. Avril was riding at a constant speed.
Which function can be used to find d, the total distance she traveled in x hours?
Choose:
d = 4x
d = x + 15
d = 4 + x
x = 4d
d=4x
400
How do you determine if a GRAPH is a function or not?
What is the Vertical Line Test?
400
Does the following table represent a function?
x y
1 2
2 5
6 2
2 9
5 1
What is No, because the input (x) of 2 has two different outputs (y)?
400
Evaluate this function for P(50)
F(x)=-1/2x^2+5x+2
P(50)=-998
400
When is this function decreasing?
-6<x<-4, -2<x<2, 5<x<6
400
Find the DOMAIN:
-5<=x<=8 or (-5,8]
400
Determine the domain, range, and vertex of the function below:
h(x) = -5abs(x+7) + 45
Then find h(2). Enter your answer as a number.
d: ARN
r: y<=45
h(2) = 0
400
Shrimp can be purchased for $14/lb and crab legs for $20/lb at the local grocery market. If you have $560 to spend on seafood for your gathering, write an equation that will be able to determine the various possibilities for your purchase, letting x be the number of pounds of shrimp. (yes, you are spending it all)
Also determine the intercepts and what they mean in context of the story.
14x + 20y =560
You can get 40 lbs of shrimp if you don't get any crab legs, or you can get 28 lbs of crab legs if you don't get any shrimp.
500
This word describes any set of ordered pairs where each x-value is paired with one y-value.
What is a Function?
500
Is this a function and why?
What is no, because x's repeat at 8?
500
Find f(4) =
0
500
f(x) = -2x^2 + 12x + 16
What is the end behavior of this function?
As x goes to pos infinity, y goes to neg infinity.
As x goes to neg infinity, y goes to neg infinity.
500
Find the RANGE:
-3<=y<=2 or (-3, 2]
500
f(x) = -abs(x + 1)-7 and g(x) = 4abs(x -7) + 1
Compare the functions above with 3 items, and one cannot be the domain.
answers may vary:
g(x) has a range that is y>=1 while f(x) has a range that is y<=-7.
g(x) has a vertex at (7,1) where f(x) has a vertex at (-1,-7)
g(x) is narrower than f(x)
f(x) opens down and g(x) opens up
500
Shrimp can be purchased for $14/lb and crab legs for $20/lb at the local grocery market. If you have $480 to spend on seafood for your gathering, write an equation that will be able to determine the various possibilities for your purchase letting x be the number of pounds of shrimp. (yes, you are spending it all)
Would this domain be discrete or continuous? Why?
Continuous because you can buy partial pounds of seafood.