Polynomial Functions
Operations on Functions/Inverses
Radical Expressions/Equations
Graphing Functions
Exponential/ Logarithmic Functions
100
Identify the real zeros of f(x)=x3 - 8x2 + 12x
0, 2, 6
100
If f(x)=3x2 - 5x + 9 and g(x)=2x + 7, find (f o g)(-2).
21
100
Simplify.
3/-48v9z14
-2v3z4 3/6z2
100
Draw a sketch of each parent function listed below.
y=2/x
y=2x
y=log2x
(Check graphs)
100
Solve 2 + ex>9
x>ln7
200
Identify the intervals over which the graph is increasing and decreasing.
Increasing: (0, 2)
Decreasing (-inf, 0), (2, inf)
200
If f(x) = 3x - 2 and g(x) = -x2 + 4, find (f o f)(x).
(f o f)(x)= 9x - 8
200
The measures of the legs of a right triangle are 6x2y and 9x2y. Write a simplified expression that represents the length of the hypotenuse of the triangle.
3x2y 2/13
200
Graph y = 2x+5. Identify the domain and range.
Key points: (-6, 1/2), (-5, 1), (-4, 2)
Horizontal asymptote: y=0
Domain: (-inf, inf)
Range: (0, inf)
200
If you deposit $2000 in an account paying 6.4% interest compounded continuously, how long will it take for. your money to triple?
About 17.2 years
300
Identify the end behavior of f(x) = 8x2 - x5 + 3x - 9.
As x-->-inf, f(x)-->inf
As x-->inf, f(x)-->-inf
300
If f(x) = 3x - 2 and g(x) = -x2 + 4, find (g o f)(x).
(g o f)(x)= -9x2 +12x
300
Simplify.
4/(8 / 9a3)
4/(72a) / 3a
300
Graph y = - 2/(2x-3) -1. (You may not graph in your calculator). Then, state the domain and range.
Key points: (1.5, -1), (2, -2), (3.5, -3), (6, -4)
Domain: [1.5, inf)
Range: (-inf, -1]
300
A certain culture of bacteria will grow from 250 to 2000 bacteria in 1.5 hours. Find the constant k for the growth formula.
k = 1.3863
400
(x + 4) is a factor of f(x) = 3x3 - x2 - 62x - 40. Find the remaining factors.
(3x + 2)(x - 5)
400
If f(x) = 5x - 3, find f-1(x).
f-1(x)= 1/5x + 3/5
400
Solve 2/(3x+1) = 2/(5x) - 1
x = 5
(x=0 is an extranneous solution)
400
Graph f(x)= log4(x + 3) - 2
Key points: (-2.75, -3), (-2, -2), (1, -1)
Vertical Asymptote: x= -3
Domain: (-3, inf)
Range: (-inf, inf)
400
You deposited $1000 into an account that pays an annual interest rate of 5% compounded quarterly. How long will it take for your money to double?
about 13.9 years
500
Solve 100x = -12x3
x= 0, +5isqrt3/3
500
If f(x) = log3(x + 1), find the inverse of f.
f-1(x)= 3x - 1
500
Solve.
3 2/(2x-1) + 6 < 15
1/2 < x < 5
500
Graph f(x)= x4 - 29x2 + 100 using its zeros, end behavior, and a table of points. You may NOT graph in your calculator.
zeros: -5, -2, 2, 5
500
2y+3 > 83y
y < 0.3750