Semester 2 Final Review

Rational Functions

100

Describe the transformations of the function 

f(x)=-2/(x+1)+3

reflected over the x axis, stretched by a factor of 2, left 1, up 3

Parent funciton 

y=1/x

200

What are the domain and range of the function 

f(x)=1/x

Domain: 

{x|x≠0}

Range: 

{y|y≠0}

300

Does the function have a hole? If so, where?

f(x)=(x^2-3x-4)/(x+4)

No Hole!

Radicals

100

Write the rational expression in exponential form 

root(4)(x^7)

x^(7/4)

200

What is the equation of the cube root function shifted right by 5 units, up by 7 units, and stretched by a factor of 3?

3root(3)(x-5)+7

300

Solve the radical equation

4=root()(5(x-4))-2

x=11.2

Logs/Exponential Functions

100

Write this logarithmic equation in exponential form 

ln4=x

e^x=4

200

Expand the logarithm.

log((x+3)/(5x)^3)

log(x+3)-(3log(5)+3log(x))

300

Write as a single logarithm in condensed form (argument should be simplified) 

4(log_3x+5log_3y)-6(2log_3y+log_3x)

log_3(y^8/x^2)

Solving Equations

100

32^(x+6)=16^(x+3)

x=-18

200

What is the solution to the equation 

(3x-1)/(x(x+3))+5/x=8/x

No Solution

300

Solve for x. Round to the nearest thousandth.

3^(x+1)=7

x=0.771