Building Functions
Identify the types of functions present in the equation below (ex. polynomial, logarithmic, exponential).
A(x) = (3x-2cos(x)) / (x^2 - 4)
There are two polynomial functions (3x, x^2 - 4) and one trigonometric function (cos(x)).
Evaluate the following.
f(x) = 1 - x
g(x) = 1 + x
f(g(x)) = ?
f(g(x)) = -x
Evaluate.
7^x * 7^y = ?
7^(x + y)
Simplify.
f(x) = (x^2 - 5x + 6) / (x - 3)
x - 2 (given x =/= 3)
Name the first five prime numbers.
2, 3, 5, 7, 11.
Identify the types of functions present in the equation below (ex. polynomial, logarithmic, exponential).
A(x) = 1/3 arcsin(3x)
There is one polynomial function (3x) and one trigonometric function (arcsin(x)).
Write m in terms of y using the following.
m = 3k + 2
k = x^2 - 1
x = y + 1
m = 3y^2 + 6y + 5
Evaluate.
(6^y)^x
6^(xy)
Simplify.
(x^2 + 10x + 25) / (x + 5)
x + 5 (given x =/= -5)
How much does a cheese coney cost at Ludlow Skyline?
$2.99 (omg)
Identify the types of functions present in the equation below (ex. polynomial, logarithmic, exponential).
A(x) = sin^2(x) + 4sin(x) - 5
There is one polynomial function (sin^2 + 4sin - 5) and one trigonometric function (sin(x)).
Evaluate the following.
f(x) = 3x - 6
g(x) = 1/3 (x + 2)
Find f(g(x)) and g(f(x)).f(g(x)) and g(f(x)) both equal x.
Evaluate.
5^x * 4^x
Simplify.
(x - 5) / (x^2 - x - 20)
1 / (x + 4) (given x =/= -4)
When rolling two fair dice, what's the most likely sum?
7
Identify the types of functions present in the equation below (ex. polynomial, logarithmic, exponential).
A(x) = |x^2sin(x) + |x| + 5|
There are two absolute value functions, one polynomial function (x^2 + x + 5), and one trigonometric function (sin(x)).
Evaluate the following.
f(x) = g(x + 1)g(y) = (y + 1)^2
f(x) = ?
f(x) = (x+2)^2
Simplify.
(60 / 3^y) ^x
Simplify.
(y^3 - y^2) / (1 - y)
y^2 (given y =/= 1)
How much does a 30-second Super Bowl commercial cost this year?
$7 million
Identify the types of functions present in the equation below (ex. polynomial, logarithmic, exponential).
A(x) = cos(4log(1/x) + (x^2+4)/(x^2-4))There is one trigonometric function (cos(x)), one rational function (or 2 polynomial functions) (x^2 +4 / x^2 - 4), one logarithmic function (log(x)), and one reciprocal function (1/x) (extra point for reciprocal).
f(x) = 3 + x^2
g(t) = 1 + 1/t
f(g(x)) = ?
f(g(x)) = (4x^2 + 2x + 1) / (x^2)
x^2x + (x^x)^2 - 32
2((x^x)^2 - 16)
(t -3) / (t + 3)
How many points did Evan McPherson score this season?
118