Unit 1 - Building Blocks
Unit 2 - Functions and Graphs
Unit 3 - Power, Polynomial, and Rational Functions
Unit 4 - Exponential and Logarithmic Functions
Miscellanous
100
Convert into scientific notation;
0.00000453
Answer;
4.53x10^-6
100
Which of the following would describe the horizontal asymptote of this function?
(6x^2-4x+11)/(3x^2+4)
A) Horizontal asymptote at y = 0
B) Horizontal asymptote at y = 2
C) Oblique asymptote
D) No horizontal asymptote
Answer;
B) Horizontal asymptote at
y=2
100
Using synthetic division, which number would go into the box _| when setting up the following example?
(4x^3-2x^2+13x-44)/(x+4)
Answer;
-4
100
Use the change of base formula to find log6129. (round to three decimal places)
Answer;
2.712
100
The graph below is which type of function?
(A) Quadratic, (B) Absolute Value, (C) Exponential, (D) Logarithmic, (E) Square Root
Answer;
(E) Square Root
200
Factor completely;
12x3 - 4x
Answer;
4x(3x2 - 1)
200
Using interval notation, identify where this graph is decreasing;
Answer;
(-4, oo)
200
Where would the following function cross the x-axis? (hint: find the zeros)
f(x)=x^2+18x+45
Answer:
After factoring;
f(x)=(x+15)(x+3)
It will cross at (-3, 0) and (-15, 0)
200
Rewrite log4 6x + log8 10 using the rules for condensing and expanding.
Answer;
Not possible
200
Is the function below even, odd, or neither?
f(x)=5x^4-10x^3-23x
Answer;
Neither
300
Simplify using imaginary units;
sqrt(-24)
Answer;
2isqrt(6)
300
Identify the end behavior of the function;
f(x)=5x^7-9x^3+x^2-19
Answer;
x->oo, y->oo
x->-oo, y->-oo
300
A power function is written as
ax^b
The sum of two or more power functions is called a ___________ function.
Answer;
A POLYNOMIAL function
300
Find the accumulated amount of an investment of $70,000 that is compounded annually at an 8.3% interest rate that grows for 5 years.
Answer;
$104,289.44
300
Identify the range of this graph using interval notation;
Answer;
(-oo,4]
400
Solve for x, write your answer in interval notation;
-2x + 5 > 15
Answer;
(-oo, -5)
400
Find the inverse of this function;
f(x)=-3x+11
Answer;
f(x)=(x-11)/-3
400
What is the oblique asymptote of this function?
(5x^2-33x-14)/(x-7)
Answer;
5x+2
400
A home that has been growing in value by 7.1% annually would have had an initial purchase price of ______ if it were sold twenty years later for $905,000.
Answer;
$229,540
400
Use the quadratic formula to find the solutions for x in this equation;
6x^2-28x-10=0
Quadratic formula;
Answer;
x=5,-1/3
500
Simplify;
(16x^5y^9)/(20xy^-4)
Answer;
(4x^4y^13)/5
500
Write the function that shows the parent graph
f(x)=x^2
with the following translations;
- Vertical reflection over the x-axis
- Vertical compression of 2
- Horizontal shift left 5
- Vertical shift up 9
f(x)=-1/2(x+5)^2+9
500
Use either long division or synthetic division to find the quotient;
(2x^3+2x^2-9x+9)/(x+3)
Answer;
2x^2-4x+3
500
Rewrite
4 logx+log9x-5logx^3
using the rules for condensing logarithms.
Answer;
9/(x^10)
500
Simplify;
i^491
Answer;
i^491=-i