Graphing and Key Features
Polynomials and Quadratics
Rational and Radical Functions
Exponentials and Finance
Systems and Word Problems
100
A function is defined as f(x)=(2x+3)^2-2 . State the interval over which the function is increasing.
[1.5,∞)
x≥1.5
100
Solve the exponential equation 6^(x-2)=216 for x.
x=5
100
State the coordinates or equation of the horizontal asymptote for the rational function f(x)2/(x-4)+3
y=3
100
Derrick invests $27,000 into a stock portfolio. If the value increases reliably by 8% every year, write the exponential function modeling his investment over time.
f(x)=27000(1.08)^x
100
A business makes ski pants (p) and ski jackets (j). Pants require 4 minutes to cut; jackets require 8 minutes. If the maximum total cutting time available is 48 minutes, write the inequality constraint
4p+8j≤48
200
What are the domain and range of the following function?
MUST GET BOTH RIGHT FOR POINTS!
f(x)=sqrt(x+1)-2
Domain:
[-1,∞)
x≥-1
Range:
[-2,∞)
y≥-2
200
Factor the following polynomial.
27x^3-64
(3x-4)(9x^2+12x+16)
200
Solve the radical equation sqrt(2x-1)=sqrt5 for x.
x=3
200
y=(1/2)^x-3 What is the end behavior (both sides) for the following equation?
x→-∞, y→∞
x→∞, y→-3
200
Sophia launches a ball into the air. Its height in feet is modeled by
h(t) = -14t^2 + 28t + 42
. What is the initial height of the platform from which she threw it?
42 feet
300
Using the function f(x)=x^4-5x^3+6x^2+4x-8 find the average rate of change from [-1,3].
average rate of change = 1
300
Find all the real and imaginary solutions for the polynomial equation x^3+4x=0
x={0,2i,-2i}
300
What are the equations of the asymptotes for this function?
f(x)=1/(x+3)+5
x=-3
y=5
300
Tyrese puts $15,000 into an account yielding 6.2% annual interest compounded monthly. To the nearest cent, how much money is in the account after 10 years?
$27,839.45
300
Carla can wash a commercial load of dishes in 42 minutes. When Dan helps her, they finish the load together in 28 minutes. How long does it take Dan to work completely alone?
84 minutes or 1 hour and 24 minutes
400
Evaluate f(2) .
f(2)=-4
400
Find the discriminant for this equation and describe the number and type of roots it will have.
y=x^2-5x+13
discriminant is 3
types of solutions - 2 irrational roots
400
How many real and imaginary solutions does the polynomial -x^5+x^3+2x^2-x=0 contain?
3 real and 2 imaginary
400
Simplify
(3+i)(3-i)
10-6i
400
Given a bounded linear programming system, you test your feasible corner vertices against the objective volume function V = 8x + 12y. Which vertex pair configuration optimizes and maximizes storage volume if the corners are (0,7), (12,0), and (8,3)?
(8,3).
500
If a table shows t(2)=-5 and t(4)=3 , what is the average rate of change over the interval [2,4] .
Average rate of change = 4
500
Find exact solutions for the following quadratic.
y=x^2-5x+13
x={(5±3isqrt3)/2}
500
If a rational function has a vertical asymptote at x=-3 and a horizontal asymptote at y=5 , what value can the function g(x) never equal?
g(x) can not = 5.
500
In the following function, f(x)=27000(.92)^x what does .92 represent?
A depreciation of 8% per year.
500
Determine if the coordinates (0,0) represent a valid solution that satisfies the system of linear inequalities
Not a solution