Domain/
Range
Range
Identify the domain of the following function and write answer in interval notation.
g(x)= 1/(x-9)
(-∞, 9) U (9, ∞)
Let f(x) = 8x + 9. What is f-1(x)?
f-1(x) =(x-9)/8
Identify the zeros of f(x) = (x + 5)2(x - 9)3 and their multiplicity. (Smallest to Largest)
x = -5 with a multiplicity of 2
x = 9 with a multiplicity of 3
Given f(x) = 2x + 5 and g(x) = x2 + 4x.
Find (f o g) (1)
(f o g) (1) = 15
Given the function: f(x) =
{2x + 2, x < 0
2x + 4, x >= 0}
What is f(-1), f(0), f(2)?
f(-1) = 0
f(0) = 4
f(2) = 8
Identify the domain of the following function and write answer in interval notation.
h(x) = √(x+6)
[-6, ∞)
Find the inverse of f(x) = 3√(11x - 6)
f-1(x) = (x3 + 6)/11
Find the quotient and remainder using synthetic division.
(x4 - 2x3 + 6x + 5)/(x + 1)
Quotient: x3 - 3x2 +3x + 3
Remainder: 2
Find the horizontal asymptote or oblique asymptote.
f(x) = (x2 + 8x + 4)/(x + 7)
y = x + 1
Determine if the functions below are even, odd, or neither without a graph.
y = 2x3 + x2
Neither
Find the domain of the function and write your answer in interval notation.
f(x) = √(-8x + 4)
(-∞, 1/2]
Find the vertex of f(x) = - (x - 7)2 - 2
(7,-2)
Is (x-1) a factor of
3x3 + x2 - 9x + 5?
Yes, it is a factor
Find the horizontal asymptote or oblique asymptote.
f(x) = (x + 4x3 - 5)/(2x3 - 3x2 -2)
y = 2
Given f(x) = x2, after performing the following transformations: shift upward 62 units and shift 73 units to the right, the new function is
y = (x - 73)2 + 62
Find the domain of f and write your answer in interval notation.
f(x) = (x + 1)/(x2 + 2x - 15)
(-∞, -5) U (-5, 3) U (3, ∞)
Write the expression in vertex form
y = 3x2 + 6x + 7
y = 3(x+1)2 + 4
Use the rational zeros theorem to list all possible zeros of the polynomial
p(x) = x3 - 5x2 + x + 10
+- 1,2,5,10
Determine the vertical asymptotes and holes (removable points of discontinuity) of the rational function shown below.
f(x) = ((x -7)(x + 10))/((x + 10)(x + 6))
Use commas to separate results if there are more than one of each. If there is not a hole or asymptote, record DNE as your answer.
Holes: x = -10
Vertical Asymptotes: x = -6
Given f(x) = x2, after performing the following transformations: stretched by 4, translated right by 9, and translated down by 1, the new function is
y = 4(x - 9)2 - 1
Find the domain and range of the following graph on the board.
Write your answer as an interval.
Domain: (-∞, -3]
Range: (-∞,∞)
Suppose a border collie jumps in the air and that its height (in meters) above the ground is given by
h = -4.9t2 + 4.5t
What is the maximum height of the border collie above the ground as it jumps? Round your answer to 2 decimal places
1.03 meters
Factor the polynomial function below. List the possible rational zeros to find the zeros and factors of the polynomial.
f(x) = 25x3 - 40x2 - 23x + 6
The zeros are 2, -3/5, 1/5
f(x) = (x-2)(5x+3)(5x-1)
Let f(x) = (x2 - 5x + 4)/(x2 - 6x + 5)
Find the domain (interval notation), holes, vertical asymptote(s), and horizontal asymptote(s).
Domain: (-∞, 1) U (1,5) U (5,∞)
Holes at x = 1
Vertical Asymptote at x = 5
Horizontal Asymptote at y = 1
Find the degree, leading term, leading coefficient, constant term, and end behavior of the given polynomial.
g(x) = x - 5x4 - 2 - 3x9
Degree: 9, Leading term: -3x9, Leading coefficient: -3, Constant term: -2
End behavior:
As x -> -∞, g(x) -> ∞
As x -> ∞, g(x) -> -∞