Function Families
Sequences
Linear Functions and Regression
Solving Linear Equations
and Inequalities
and Inequalities
Solving Systems of Equations
100
What function family would this function fall into?
Does this function have an absolute maximum or an absolute minimum?
Absolute Value Function
Absolute Minimum
100
Is the following sequence arithmetic or geometric? What is the common difference/ratio?
17, 34, 68, 136, 272...
The sequence is geometric. r=2
100
Rewrite the arithmetic sequence as a linear function.
an=3-4(n-1)
f(x)=-4x+7
100
Solve the equation:
2(x+6)=3x-1
x=13
100
Identify the solution to the system of equations.
(1,5)
200
Madison enjoys bicycling for exercise. Each Saturday she bikes a course she has mapped out around town. She averages a speed of 12 mph on her trip.
Determine the independent and dependent quantities with the appropriate units.
Independent quantity: Time (hours)
Dependent quantity: Distance (miles)
200
Is the following sequence arithmetic or geometric? What is the common difference/ratio?
1.0, 0.2, -0.6, -0.14, -0.22...
The sequence is arithmetic. d=-0.8
200
Describe the relationship between the two variables using proper terminology (Strong, weak, positive, negative) and give a possible r-value (correlation coefficient).
There is a strong, negative relationship.
Possible r-values range from r=-0.9 to r=-0.6.
200
Solve the linear inequality. Then graph on a number line.
-13+5x>=27
x>=8
200
Solve the system of equations.
2x+3y=18
y=4
(3,4)
300
In what function family does the following function belong? Would it have an absolute maximum or minimum?
y=-x^2+2x+9
Quadratic Function
Absolute Maximum
300
Write a recursive formula for the following sequence:
Determine the 6th term.
2, 5, 8, 11, 14...
an=an-1+3, a6=17
300
Write a linear function that represents the data in the table.
y=2x+5
300
Determine if the equation has one solution, no solutions or infinitely many solutions.
-3(4-2x)=2(3x-6)
Infinitely Many Solutions
300
Solve the system of equations.
y=4x+22
y=-2(-11-2x)
Infinitely many solutions.
400
Of the six relations present, how many of them are functions?
There are 3 functions and 3 relations that are not functions.
400
Write an explicit formula for the following sequence and determine the 11th term.
2,10,50,250,1250...
g11=19531250
gn=2*5^(n-1)
400
Nathan has sixty pieces of candy to give out on Halloween. Each kid that trick or treats at his house is given two pieces of candy. Write a linear function to represent the amount of candy Nathan has. How many kids will Nathan have given candy to when he has 32 pieces left.
14 kids
y=-2x+60
400
Solve the equation:
5n+34=-2(1-7n)
n=4
400
Solve the system of equations.
3x-4y=-13
-3x+5y=20
(5,7)
500
Is the following function always increasing, always decreasing, constant, or a combination? Justify your answer.
y=0.3^x
Because 0.3<1, this function represents exponential decay and will always decrease.
500
Write an explicit formula for a sequence that represents the pattern in the picture below. Find the 25th term.
an=8+4(n-1)
a25=104
500
A Christmas tree farmer plants trees that are 2 feet tall. 3 weeks later, they are 11 feet tall. Determine the average rate of change in terms of units given in the scenario. Determine how tall the trees will be after 7 weeks.
Average Rate of Change: 3 feet per week
Height after 7 weeks: 23 feet tall
500
Solve the compound inequality.
17<=-2x+5<=27
-11<=x<=-6
500
Solve the system of equations:
3x-5y=6
-4x+2y=6
(-3,-3)