Graphing Rational Functions
Rational Inequality
Composite Function
Inverse Functions
Other
100
f(x)= x/(3x-15)
FIND:
1. Domain
2. Vertical asymptote
3. Holes
4. Horizontal asymptote
1. Domain: (-infinity, 5) U (5, infinity)
2. Vertical asymptote: x=5
3. Holes: DNE
4. y= 1/3
100
Solve the rational equation. Be sure to check for extraneous solutions.
x/(5x + 4)= 5
x=-5/6
100
Let
f(x) = 3x − 6, g(x) = |x|, h(x) = sqrt of x and k(x) = 1/x
Find and simplify the indicated composite function.
(h ∘ g ∘ k)(x)
sqrt of 1/(|x|)
100
Find the inverse. Check your answer algebraically and graphically.
f(x) = 1 − (3 + 2x)/4
f ^−1(x) =
-2x + 1/2
100
Solve the following equation. (Enter your answers as a comma-separated list.)
x^2/3=1
x= -1,1
200
f(x) = 4 + 7x/(6 − 4x)
FIND:
Domain
VA
Holes
HA
Domain: (-infinity, 3/2) U (3/2, infinity)
VA: x=3/2
Holes: DNE
HA: y= -7/4
200
Solve the rational equation. Be sure to check for extraneous solutions.
8x − 3/(x^2 + 12) = 1
x=3 x=5
200
Let
f(x) = 5x − 3, g(x) = |x|, h(x) = sqrt of x
and k(x) = 1/x
Find and simplify the indicated composite function.
(f ∘ g ∘ h)(x)
5(sqrt of x)-3
200
Find the inverse. Check your answer algebraically and graphically.
f(x) = 9(x + 4)^2 − 2, for x ≤ −4
f^-1(x)=
-sqrt(x+2/9)-4
200
Solve the following equation. (Enter your answers as a comma-separated list.)
sqrt(x − 4) + sqrt(x − 7)=3
x= 8
300
f(x) = x^3 + 1/(x^2 − 1)
FIND:
Domain
VA
Holes
HA
Domain: (-infinity, -1) U (-1,1) U (1, infinity)
VA: x=1
Hole: (-1, -3/2)
HA: DNE
300
Solve the rational inequality. Express your answer using interval notation.
x − 3/(x + 2)≤ 0
(-2,3]
300
Write the following as a composition of two non-identity functions.
(g ∘ f)(x) = h(x) = sqrt of 9x − 5
f(x)=9x-5
g(x)= sqrt of x
300
Find the inverse. Check your answer algebraically and graphically.
f(x) = 7/(x − 3)
f^-1(x)=
7/x + 3
300
Solve the following equation. (Enter your answers as a comma-separated list.)
8 − (4 − 2x)^2/3 = 4
x=-2,6
400
f(x) = x^3 + 4x^2 + 3x/(x^2 − 2x − 3)
FIND
Domain
VA
Hole
HA
Domain: (-infinity, -1) U (-1,3) U (3, infinity)
VA: x=3
Hole: (-1,1)
HA: DNE
400
Solve the rational inequality. Express your answer using interval notation.
x/(x^2 − 16)> 0
(-4,0) U (4, infinity)
400
Let f be the function defined by
f = {(−3, 5), (−2, 4), (−1, 7), (0, −1), (1, 5), (2,7), (3, −1)}
and let g be the function defined
g = {(−3, −3), (−2, 8), (−1, −1), (0, 2), (1, −1), (2, 7), (3, 2)}.
Find the following value if it exists. (If an answer does not exist, enter DNE.)
(f ∘ f)(0)
7
400
Find the inverse. Check your answer algebraically and graphically.
f(x) = 4x + 3/(3x − 2)
f^-1(x)=
2x+3/(3x-4)
400
Solve the following inequality.
2(x − 2)^−1/3 − 2/3x(x − 2)^−4/3 ≤ 0
(-infinity, 2) U (2,3)
500
Use the six-step procedure to graph:
f(x) = 1/(x^2 − 36)
500
Solve the rational inequality. Express your answer using interval notation.
2x^3 + 3x^2 − 5x/(5x^2 + 11x + 6)> 0
(-5/2,-6/5) U (-1,0) U (1, infinity)
500
Let
f(x) = 5x − 4, g(x) = |x|, h(x) = sqrt of x
and k(x) = 4/x
Find and simplify the indicated composite function.
(f ∘ k)(x)
20-4x/(x)
500
Find the inverse. Check your answer algebraically and graphically.
f(x) = −6x − 5/(x + 6)
f^-1(x)=
-6x-5/(x+6)
500
Find the inverse of
k(x) = 2x/sqrt(x^2 − 1)
k^-1(x)= x/sqrt(x^2-4)