Linear versus Exponential Functions
Quadratic Functions
Exponents and Radicals
Functions and Their Behaviors
Data Analysis & Probability
100
Is this function linear or exponential?
Exponential
100
Find the vertex of y=5(x+2)^2+6
(-2,6)
100
Simplify y^6-:y^2xxy^0
y^(6-2+0)=y^4
100
Identify the domain of the following function.
-3<x<=1
(-3,1]
100
What kind of data is displayed below?
Remember: data can be univariate/bivariate and categorical/numerical.
Categorical bivariate
Two-way table or joint relative frequency table
200
If f(x)=3x and g(x)=3^x , then what is g(5)-f(5) .
228
g(3)-f(3)=3^5-3(5)
243-15=228
200
How many solutions does the function y=-3x^2+10x-7 have?
Two solutions
b^2-4ac
(10)^2-4(-3)(-7)
100-84=16
200
Evaluate ((-3)^2)^4
(-3)^8=6561
200
Is this a function?
FULL POINTS: Why or why not?
Yes. Each input has only one output.
200
The number of cars sold in a week at a large car dealership over a 20-week period is given below.
16 12 8 7 26 32 15 51 29 45 19 11 6 15 32 18 43 31 23 23
Which data display would you use to represent this data
This data is numerical and univariate.
Acceptable answers: histograms, box plot, stem-and-leaf, line plots
300
Write the equation of a linear function with a slope of -3/4 and passes through (4,4) in point-slope form.
Double Points: Write in slope-intercept form.
Triple Points: Write in slope-intercept AND standard form.
Point-Slope Form:
y-4=-3/4(x-4)
Slope-Intercept Form:
y=-3/4x+7
Standard Form:
3x+4y=28
300
Write the equation of a quadratic function with the vertex (-4, 2) and a leading coefficient of 1.5
DOUBLE POINTS: Write the equation in standard form.
y=1.5(x+4)^2+2
DOUBLE POINTS:
y=1.5x^2+12x+26
300
Write 5^(-5/2) with repeated multiplication.
1/sqrt(5*5*5*5*5)
300
Given the function g(x)=2|x+2|+1 , find g(1) .
g(1)=2|1+2|+1
g(1)=2|3|+1=6+1
g(1)=7
300
Dr. Larry has noticed that when he carries around his lucky rock, his students seem to be nicer to him. Can one conclude that this positive correlation shows a causal relationship?
a. Yes, because Larry decides whether or not to put his lucky rock in his pocket before he encounters people during the day.
b. Yes, because it is not a negative correlation.
c. No, because lucky rocks only work for children.
d. No, because it is possible that people are nice to Larry because of another factor that
also causes him to put the rock in his pocket.
d. No, because it is possible that people are nice to Larry because of another factor that also causes him to put the rock in his pocket.
400
Write the equation of an exponential function with an initial value of 5 and a decay rate of 5%.
5(1-0.05)^x
or
5(0.95)^x
400
Using the quadratic formula, find the roots of the function f(x)=4x^2-12x+9 .
(-(-12)+-sqrt((-12)^2-4(4)(9)))/(2(4))
(12+-sqrt(144-4(4)(9)))/8=(12+-sqrt(144-144))/8
(12+-0)/8=128=3/2=1.5
400
Solve for r
I=P/(4pir^2)
r=sqrt(P/(4piI)
400
What is the range of the parent function y=root(3)(x) ?
x>=0
[0,infty)
400
Crickets are known for many things, most notable for their sound. Fun fact, they won't chirp when it's below 40 degrees nor above 100 degrees. The relationship between the number of chirps per minute (x) and the temperature (y) can be modeled by the function y=0.214x+32.317. The graph of certain data points and their residuals can be found below.
Given the table and graph, describe the strength and direction of correlation.
BONUS 250 POINTS: Are there any potential outliers?
There is a strong positive correlation between the average chirps per minute and the temperature outside.
BONUS: 140 chirps per minute, 80 degrees
500
Did you know that cities and states can have sisters? One such example is the state of Florida and the state of Nueva Esparta in Venezuela. In 1990, Florida has a population of approximately 12.9 million residents and has increased about 297 thousand residents each year. In contrast, Nueva Esparta had a population of about 260 thousand residents and has increased about 3.2% each year. According to the models, which state will have the higher population in the year 2200?
DOUBLE POINTS: By how much?
Nueva Esparta (approx. 194.0 million) > Florida (approx. 75.3 million)
Difference of approximately 118.7 million
500
In an effort to catch a criminal; a superhero is going to leap over a building and take a short cut down the ally. The function f(x)=-16x^2+150x gives the superhero's height in feet as a function of time. The building is 425 feet high.
Half Points: Will the superhero make it over the building?
Full Points: how high can the superhero jump?
Nope. The superhero can only jump about 351.6 feet.
500
(12mn^6-40m^2n^3)/(4m^2n^3)
(12mn^6)/(4m^2n^3)-(40m^2n^3)/(4m^2n^3)
(3n^3)/(m)-10
500
If I had some function f(x) , what type of transformation is indicated by k*f(x) ?
Transformations include translation (horizontal/vertical), dilation (horizontal/vertical), reflection (horizontal/vertical).
Vertical dilation
500
Find the mean given the following table.
((0*31)+(1*8)+(2*3)+(3*4)+(4*1)+(5*3))/(31+8+3+4+1+3)
(0+8+6+12+4+15)/50
45/50=0.9~~1
750
Carbon-14 (also known as radiocarbon) has a half life of approximately 5700 years. If 2 kilograms of the material was collected, how much of it would be left after 85,500 years?
85,500 years = 15 half-lives
2 kilograms = 2000 grams
2000(1/2)^15~~0.061
750
Write a function given the following table. 
Vertex is (-3, -4)
Leading coefficient is 1
y=(x+3)^2-4
750
Expand y=a(x-h)^2+k
y=ah^2-2ahx+ax^2+k
750
Describe the transformation(s) between f(x) and g(x) .
f(x)=|x|
g(x)=-|x-2|+4
Vertical reflection
Horizontal translation 2 units to the right
Vertical translation 4 units up
750
Of the students who do not like snowmobiles, what percent of them also do not like skateboards.
Students who do not like snowmobiles = 55
Students who do not like snowmobiles and skateboards = 10
10/55=0.bar18=18.bar18%~~18.2%