Concept Review for Chapter 3

Building Functions

100

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)).

200

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)).

300

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)).

400

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)).

500

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).

Composition of Functions

100

Evaluate the following.

f(x) = 1 - x

g(x) = 1 + x

f(g(x)) = ?

f(g(x)) = -x

200

Write m in terms of y using the following.

m = 3k + 2

k = x^2 - 1

x = y + 1

m = 3y^2 + 6y + 5

300

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.

400

Evaluate the following.

f(x) = g(x + 1)

g(y) = (y + 1)^2

f(x) = ?

f(x) = (x+2)^2

500

Evaluate the following.

f(x) = 3 + x^2

g(t) = 1 + 1/t

f(g(x)) = ?

f(g(x)) = (4x^2 + 2x + 1) / (x^2)

Exponential Identities

100

Evaluate.

7^x * 7^y = ?

7^(x + y)

200

Evaluate.

(6^y)^x

6^(xy)

300

Evaluate.

(5 * 4)^x

5^x * 4^x

400

Simplify.

(5^x * 12^x) / (3^xy)

(60 / 3^y) ^x

500

Simplify.

x^2x + (x^x)^2 - 32

2((x^x)^2 - 16)

Simplifying Rational Functions

100

Simplify.

f(x) = (x^2 - 5x + 6) / (x - 3)

x - 2 (given x =/= 3)

200

Simplify.

(x^2 + 10x + 25) / (x + 5)

x + 5 (given x =/= -5)

300

Simplify.

(x - 5) / (x^2 - x - 20)

1 / (x + 4) (given x =/= -4)

400

Simplify.

(y^3 - y^2) / (1 - y)

y^2 (given y =/= 1)

500

Simplify.

(t^2 - 9) / (t^2 + 9 + 6t)

(t -3) / (t + 3)

Fun/Random

100

Name the first five prime numbers.

2, 3, 5, 7, 11.

200

How much does a cheese coney cost at Ludlow Skyline?

$2.99 (omg)

300

When rolling two fair dice, what's the most likely sum?

7

400

How much does a 30-second Super Bowl commercial cost this year?

$7 million

500

How many points did Evan McPherson score this season?

118