Rational Functions
Describe the parent function and 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
Write the rational expression in exponential form
root(4)(x^7)
x^(7/4)
Write this logarithmic equation in exponential form
ln4=x
e^x=4
what is the solution to the equaiton
root(3)(x+1)-2=0
x=7
What is the domain and range of the function
f(x)=1/x^2
Domain: all real numbers except 0
Range: all real numbers greater than 0
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
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)
What is the solution to the equation
(3x-1)/(x+3)=8
x=-5
Does the function have a removable discontinuity? If so, where?
f(x)=(x^2-3x-4)/(x+4)
No
What are the x and y intercepts, domain, and range of this function?
2sqrt(x+1)+4
No x int
y int: (0,6)
Domain: all real numbers greater than or equal to -1
Range: all real numbers greater than or equal to 4
What is the inverse of the function
f(x)=10^(x+1)-3
f^-1(x)=log(x+3)-1
(1/32)^(-x+6)=16^(-x-3)
x=2
What are the holes, asymptotes, and x and y intercepts of this function?
\frac{2x^{2}-18}{x^{2}-2x-3}
Hole: x=3
VA: x=-1
HA: y=2
x int: (-3,0)
y int: (0,6)
What is the inverse of this function?
f(x)=\frac{1}{5}(x+2)^3+4
f^(-1)(x)=root(3)(5(x-4))-2
What are the asymptotes, x and y intercepts, and domain and range of the function
f(x)=-log_3(x-4)
x int: (5,0)
no y int
Domain: x>4
Range: all real numbers
log_3(x^2-4)-log_3(3x+2)=1
x=10