Functions and Graphs
Polynomials and Rational Functions
Exponents and Logarithms
Algebra Review (100-300)
Trig (400-500)
Trigonometry
100
Find the domain of f(x)=√(x^2+x-12)
x≤-4 and x≥3
100
Find an equation with vertical asymptotes at x=-2 and x=1
f(x)=1/(x^2+x-2)
100
Solve for x: log2(x)+log2(x+2)=log2(x+6) (2 is the base of the log)
x=2 (x=-3 is extraneous)
100
Find the equation of a line through (4,3) and (-4,4) in slope intercept form.
y=7/8x-1/2
100
Write sec(arctan3x) as an algebraic expression.
sec(u)=√(9x^2+1)
200
Solve x-3=√(3x+1)
x=8
200
Find the coordinates of holes in the graph: (x^3+x^2-2x)/(x^3+5x^2+6x)
(0,-.5) (-2,-3)
200
Solve: 3^(1+x)=4^(2-x)
x=ln(16/3)/ln(12)
200
Find the equation of a line through (4,3) and (-4,-4) in standard form.
7x-8y=4
200
Simplify: tan^2(u)/sec^2(u)
sin^2(u)
300
What is the domain of f(x)=√(2x-9)
x≥9/2
300
Find the remainder: (3x^3-4x^2+4x+2)/(x-2)
r=18
300
Solve for x: 25^x=5^(x+1)
x=1
300
Solve for x: abs(x-4)=x^2-4x
x=4, -1
300
Simplify: sin((pi/2)-x)
cos(u) Know your cofunctions!
400
Find the inverse: f(x)=√(10x^2+5)
f^(-1) (x)=√((1/10)x^2-2)
400
What is Mr. O'Dell's acronym for analyzing the graphs of rational functions?
HVSHI
400
Solve for x: 27^(x-3)=3^2
x=11/3
400
Solve for x: 2cosx-sinx=0 on [0,2pi)
tanx=2 x=63.43 x=243.43
400
For a triangle ABC, given C=102.3°,B=28.7°,b=27.4ft, find the length of side a.
a=43.06 feet
500
Find all possible solutions: x^4-x^3-29x^2-x-30=0 Hint: x=6 and x=-5 are two of them
x=6, -5, i, -i
500
Solve: abs(x-5)>abs(x+1)
x<2
500
Re-write as a single log: log10-log5+log2
log4
500
Find cscx for angle x with (-7,2) on its terminal side.
√(53)/2
500
Find all solutions of 2cosx+sin2x=0 on[0,2pi)
x= pi/2, 3pi/2
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