Functions
Give the domain of the following relation:
{(3,5), (-6,-1), (-7,6), (4,-1), (2,-1)}
Domain: {3,-6,-7,4,2}
Use the Leading Coefficient Test to determine the end behavior of the given polynomial:
f(x) = -6x^12 + 3x^2 - 5x + 1
Falls to the left and to the right
*Find the domain of the rational function:
f(x) = (x + 8)/(x^2 - 9)
D: (-inf, -3) U (-3, 3) U (3, inf)
Write each equation in its alternate form:
4^3 = 64
log(1000) = 3
log4(64) = 3
10^3 = 1000
Determine whether the given ordered pair is a solution to the system of equations: (-1, 2)
x + 2y = 3
-x - 3y = -7
No
*Use the vertical line test to determine whether or not the following graph is a function:
It is NOT a function!
Find the zeros of the polynomial function, and give each of their multiplicities:
f(x) = 4x^2 + 16x^3
x = 0, mult = 2
x = -1/4, mult = 1
Find any vertical asymptotes of the rational function:
f(x) = x/(2x^2 + 3)
None
Find the accumulated value of an investment of $10,000 at 4% compounded continuously for 5 years, rounded to the nearest whole dollar.
Solve the system by the substitution method:
2x - 5y = -22
x = -3y
(-6, 2)
*For the given graph of f(x) where y=f(x), find f(-1)
f(-1) = 1
Divide using synthetic division:
(x^3 + 2x - 3)/(x - 2)
x^2 + 2x + 6 + 9/(x-2)
Find any horizontal asymptote of the rational function:
f(x) = 13x^2/(5 - x^2)
y = -13
*Evaluate the expressions without a calculator:
a) 1/2
b) 0
Solve the system by the addition method:
x + 5y = -8
-2x - 4y = 10
(-3, -1)
Find the inverse of the one-to-one function:
f(x) = 3 - x/2
f^-1(x) = 6 - 2x
Use synthetic division and the Remainder Theorem to find the indicated function value:
f(x) = -3x^3 + 2x^2 - x + 9; f(3)
f(3) = -57
Find the x- and y-intercepts of the rational function:
f(x) = (x^2 + 6x + 8)/(x^2 + 4)
x-intercepts: (-2,0), (-4, 0)
y-intercept: (0,2)
*Use properties of logs to expand the given logarithmic expression:
-2log(a) + 3log(b) - log(c)
*Give the order of the matrix and identify the given element of the matrix:
a32 = 0
For the given functions f and g, find the composition:
(gof)(0)
f(x) = 7x - 1, g(x) = 2x^2 + 3
(gof)(0) = 5
Find all zeros of the polynomial:
2x^3 - 3x^2 - 32x - 15
x = -3, -1/2, 5
Find all asymptotes of the rational function:
f(x) = (x^2 - 9)/(x^2 + 6x + 9)
Vertical asymptote: x = -3
Horizontal asymptote: x = 3
Solve the logarithmic equation:
log(x + 7) - log(3) = log(7x + 1)
x = 5
*Find the product BA, if possible:
-6 3
2 -14