Austin Powers
Radical!
Lo-Lo-Lo-Logarithm
Equally Expressionate
Basic Math
100
Factor: 4y2 - 16
Hint: Difference of Squares
(2y-4)(2y+4)
100
f(x)=2x g(x)=2x-3+5
What transformation happened to g(x)?
Shift up by 5
Shift right by 3
100
Solve,
(1/4)x=1/64
Hint: Use Power properties or Log
x=3
100
Simplify,
(3x+2)(4x-2)
12x2+2x-4
100
Combine the fractions, 3/x + 1/4
Hint: Adding fractions
(12+x)/4x
200
Solve for x,
x1/2-10=50
Hint: Isolate x and then power properties
x=3600
200
What is the inverse of
f(x)=x1/4
Hint: Switch x & y
f-1(x)=x4
200
A parent logarithmic function f(x) goes through (1,0) a transformed logarithmic function g(x) goes through (3,3). What is the equation of the transformed function?
Hint: Properties of logarithms and transforamtions
Desmos visual*
f(x)=log(x) g(x)=log(x-2)+3
200
Solve for roots,
x2-3x-7
Hint: Quadratic Formula
x={-1.54,4.54}
200
Solve for x, (5x-1)/(3+x)=1/5
x=1/3
300
Define a function,
f(x)=x1/3
Draw what it looks like shifted to the right by 5 and give the equation
f(x)=(x-5)1/3
300
Convert the logarithmic equation to exponential form,
log4x+3(6)=4y
Hint: Circle method
(4x+3)4y=6
300
Solve for x,
ex=2
Hint: Properties of the natural base, e
x=ln(2)=.69
300
What are the imaginary solutions?
x2+3x+7
Hint: Quadratic Formula
300
Solve for x,
3|x-3|+2=17
x={8,-2}
400
Solve for x,
2x-5=8x-3
Hint: Same bases
x=2
400
What is the sum?
5/(x+2) + 3/(x+1)
Hint: Recall how to add fractions
(8x+11)/(x2+3x+2)
400
Solve for x,
ln(x)=3
Hint: loge is equivalent to ln
x=e3=20.08
400
Give an example of a quadratic with an imaginary solution (one that hasn't been used before)
Answer verified by instructor
400
Solve for x, 1/3x + 1/4x =6
x=7/27=.259
500
Factor,
27x3+8
(3x+2)(9x2-6x+4)
500
Give all the asymptotes of, 1/(x2-4)
y=0
x=2
x=-2
500
Explain why, -5log(x)/x
Has 2 asymptotes, give those asymptotes
y=0, x=0
Logarithm has asymptote of y=0
Rational has asymptote of y=0, x=0
500
What is the solution of,
3y+4x=9
y-x=0
(1.286, 1.286)
500
Give the equation of a circle with radius of 9
Hint: Recall radius is half of a circle
x2+y2=32