Identifying Functions in Patterns
Reading Graphs
Parts of an Equation
Domain & Range
Mixed Bag
100
Name the 3 different types of functions we've learned about.
Linear, Exponential, and Quadratic
100
Which rock is launched from a higher height? How do you know?
Rock B is because it is launched from 5 feet while Rock A is launched from 4 feet. The constant term of the equation is the y-intercept/initial height.
100
What is the meaning of the "6"?
The 6 is the initial height of the football or the y-intercept.
100
What axis is domain and what axis is range?
Domain: x-axis, Range: y-axis
100
Given a rectangle's length and width, what is the formula for its area?
Area = length x width
200
Describe how an exponential function grows.
An exponential function multiplies or divides by a common factor, which can be a fraction or whole number.
200
Which rock is launched with a greater initial velocity? How do you know?
Rock A is launched with a greater velocity because 30t is greater than 20t, which is Rock B's initial velocity.
200
What is the meaning of the "75t"?
The 75t represents the initial velocity of the football.
200
If the domain of a graph is from 0 to 20, write that using interval notation.
[0, 20]
200
True or False? The football is in the air for 4 seconds. Explain.
False, the football lands after 2.057 seconds.
300
Identify what type of function this pattern shows AND how you know.
This pattern shows a quadratic function because there is a square in each step, representing x2. There is a constant difference of differences, +2.
300
Given Rock A is the GREEN curve and Rock B is the BLUE curve, which rock lands first? How do you know?
Rock B lands first because it lands around 1.5 seconds (x-intercept) while Rock A lands around 2 seconds.
300
What is the meaning of the "-16t2"?
The -16t2 represents the force/effect of gravity.
300
Assuming the x-axis is time, identify the appropriate domain of this parabola.
[0, 2.057] (Remember, time cannot be negative!)
300
Where is the vertex on this graph and is it a maximum or minimum?
The vertex is at: (0.938, 20.063) and it is a maximum.
400
Write an equation to model this pattern.
f(x) = x2 + 2
400
What is the starting height of the football in feet?
6 feet
400
The negative sign in front of 16t2 means the parabola opens which way? Up or Down?
The parabola opens down with a maximum.
400
Assuming the y-axis is height, identify the appropriate range of this parabola.
[0, 20.063] (Remember, height cannot be negative!)
400
What does the point (2.057, 0) mean in this context? What is another term for this point?
The object is on the ground at 2.057 seconds. This is an x-intercept/zero.
500
How many squares would there be in the 25th step?
At the 25th step, 252 + 2 = 627 squares.
500
How many zeros are there and how many make sense in this context?
There are 2 zeros/x-intercepts at (-0.182, 0) and (2.057, 0) but only (2.057, 0) makes sense.
500
Write a possible equation for a 🏈 that has an initial velocity of 40 and an initial height of 5 feet.
Answers may vary but a correct response must have:
- A negative sign in front of the quadratic term
-A "40t" term
-A "+5" term
500
Write both the domain and range of this parabola.
Domain: [0, 18]
Range: [0, 80,000]
500
Beth wants to build a garden with 34 meters of fencing. Draw a possible plan for her garden.
Answers may vary but all 4 sides should add up to 34 meters.