Algebra 2 Final Prep

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)=2^x g(x)=2^x-3+5

What transformation happened to g(x)? $f(x)=2^x\quad\quad g(x)=2^{x-3}+5$

Shift up by 5

Shift right by 3

100

Solve,

(1/4)^x=1/64

$\left(\frac{1}{4}\right)^x=\frac{1}{64}$

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

$\frac{3}{x}+\frac{1}{4}$

Hint: Adding fractions

$\frac{12+x}{4x}$

(12+x)/4x $\frac{12+x}{4x}$

200

Solve for x,

x^1/2-10=50

Hint: Isolate x and then power properties

x=3600

200

What is the inverse of

f(x)=x^1/4

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

$f(x)=log(x)\quad\quad g(x)=log(x-2)+3$

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

$\frac{5x-1}{3+x}=\frac{1}{5}$

x=1/3

300

Define a function,

f(x)=x^1/3

Draw what it looks like shifted to the right by 5 and give the equation

$f(x)=(x-5)^{\frac{1}{3}}$

f(x)=(x-5)^1/3

300

Convert the logarithmic equation to exponential form,

log_4x+3(6)=4y

Hint: Circle method

(4x+3)^4y=6

300

Solve for x,

e^x=2

Hint: Properties of the natural base, e

x=ln(2)=.69

300

What are the imaginary solutions?

x²+3x+7

Hint: Quadratic Formula

$\frac{-3\pm \sqrt{3^2-4(1)(7)}}{2}=\frac{-3\pm i\sqrt{19}}{2}$

300

Solve for x,

3|x-3|+2=17

$3|x-3|+2=17$

x={8,-2}

400

Solve for x,

2^x-5=8^x-3

Hint: Same bases

x=2

400

$\frac{5}{x+2}+\frac{3}{x+1}$

What is the sum?

5/(x+2) + 3/(x+1)

Hint: Recall how to add fractions

$\frac{5}{x+2}+\frac{3}{x+1}$

$\frac{8x+11}{x^2+3x+2}$

(8x+11)/(x²+3x+2) $\frac{8x+11}{x^2+3x+2}$

400

Solve for x,

ln(x)=3

Hint: log_e 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

$\frac{1}{3x}+\frac{1}{4x}=6$

x=7/27=.259

500

Factor,

27x³+8

(3x+2)(9x²-6x+4)

500

Give all the asymptotes of, 1/(x²-4)

$\frac{1}{x^2-4}$

y=0

x=2

x=-2

500

Explain why, -5log(x)/x

$\frac{-5\cdot log(x)}{x}$

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

$\begin{cases} & 3y+4x=9 \\ & y-x=0 \end{cases}$

(1.286, 1.286)

500

Give the equation of a circle with radius of 9

Hint: Recall radius is half of a circle

$x^2+y^2=3^2$

x²+y²=3² $x^2+y^2=3^2$