Solving Equations
Evaluating Functions and compositions
Absolute Value Functions
Linear Modeling
Inverse Functions
100
Given 3(x-2)+5=20, solve for x
x=7
100
Given f(x)=3x-2, evaluate f(-2)
-8
100
What is the vertex of the following function
y=|x|-4
(0, -4)
100
Faith started the day with 120 pieces of candy and it's time to trick or treat. It is Halloween so she knows her neighbors are going to give her even more pieces of candy throughout the night. She can use the following equation to determine the total pieces of candy that she will have at the end of the night with p representing every house that she tricks or treats at.
c=15h+120
What is the slope of the linear model? What does the slope represent in the context of the problem?
slope is 15
every house she goes to will give her 15 more pieces of candy
100
What is the inverse of f(x) = 3x-2
f-1(x)=(x+2)/3
200
Given, |x-3|-5 =23, solve for x
x=31, x=-25
200
Given the following functions
f(x) = x - 6
g(x) = 2x + 5
Evaluate f(g(2))
3
200
What transformations occurred?
f(x)=-|x-4|+15
Reflect over the x axis
Right 4
Up 15
200
Tylie's parents are saving to buy a new car for her 16th birthday. The function y=125x+3200 represents the relationship between the number of months her parents have been saving and the amount in their account.
What is the slope and y-intercept? What do they represent?
slope: 125
Each additional month the savings account will increase by $125.
y-intercept: $3200 which is what they started the account with at 0 months
200
What is the inverse of g(x)=2x-4 (in simplest terms!)
g-1(x)=(x/2) + 2
300
Given -4|2x-3|>-40 solve for x
x=13/2, x=-7/2
300
Given the following functions
f(x) = -2x
g(x)=3x-10
Evaluate g(f(-3)
8
300
Determine the domain and range of the following:
y=|x-3|-5
Domain: all real numbers
Range: y>=-5
300
The following table below shows the altitude of a plane once it begins its descent to a runway.
Time Altitude
0 28500
1 26378
2 24105
3 21774
4 19452
5 17991
Find the equation for the line of best fit (round to 2 decimal places)
y=-2161.54x+28437.19
300
Find the inverse of g(x) = (1/2)x-5
g-1(x)=2x+10
400
Given -4|2x+1|-10=-30, Solve for x.
x=2, x=-3
400
Given the following functions
f(x) = 4x
g(x) = -x-8
Find (fog)(x)
(fog)(x)=-4x-32
400
Graph f(x)= -|x-2|+3
400
The table shows the income for an employee over his first 8 years of work. Find the linear regression equation and determine the correlation coefficient.
y=2714x+41461
yes because the correlation coefficient is .992
400
Are the following inverses?
f(x)=5x+15
g(x)=(1/5)x-3
yes!
500
Given 10-2|x-3|=54
No Solution!
500
Given the following functions
f(x) = 4x
g(x) = -x-8
Find (gof)(x)
(gof)(x)=-4x-8
500
What transformations occurred in the following function: f(x)=-2|x-1|-2
Reflect over the x axis,
Vertical Stretch of 2
Right 1
Down 2
500
To estimate the ages of trees forest rangers use a linear model that relates tree diameter to age. The model is useful because tree diameter is much easier to measure than tree age (which requires special tools for extracting a representative cross-section of the tree and counting the rings). Use the data in the table below collected for a certain variety of oaks to answer the following question.
Estimate the age of an oak tree whose diameter is 18 inches
116 years
500
Are the following inverses of each other?
f(x)=4x-2
g(x)=2x+4
No!