Functions

Vocabulary

100

The graph of a ______ function is a non-vertical line or part of a line.

Linear

200

The _____ of a function consists of the set of all output values 

Range

300

An ordered list of numbers that often form a pattern.

Sequence

400

Distinct isolated points.

Discrete

500

Another way to decide a relation is a function is to analyze the graph of the relation using the _____________.

Vertical Line Test

Function rules

100

Does this set of ordered pairs represent a linear function? why or why not?

(0,2)(1,4)(3,5)(1,8)

No this is not a function. Y-values increase different amounts. 

200

What is the function rule? 

(0,5)(1,8)(2,11)(3,14)

y = 3x + 5

300

What is the function rule?

(0,43)(1,32)(2,21)(3,10)

y = -11x + 43

400

What is the function rule?

(0,0)(1,4)(2,16)(3,36)(4,64)

y = 4x²

500

What is the function rule? 

(1 , 2/3) (2 , 4/9) (3 , 8/27) (4, 16/81)

y = (2/3)^x

Word Problems

100

2.5 more than the quotient of h and 3

y = h/3 + 2.5

200

The length of the rectangle is 5 more than 2 times its width. Write a function rule for the area of the rectangle.

A = 2w² + 5w

300

A car rental company charges a base fee of $30 plus $0.50 per mile driven. Write a function rule to represent the total cost (c) of renting a car for x miles. What would be the total cost for a 100-mile trip?

y = 30 + .50x

x=100 y=80

400

You buy x pounds of cherries for $2.99/lbs. What is the function rule for the amount of change C you receive from a $50 bill?

C = 50 - 2.99x

500

The recommended dosage D, in milligrams, of a certian medicine depends on a persons body mass m, in kilograms. The function D = 0.1m² + 5m  represents this relationship. 

a) What is the recommended dosage for someone whose mass is 60kg? 

b) If 1 lbs = 0.45 kg, what is the recommended dosage for someone who weighs 200 lbs?

a) 660 mg

b) 1260 mg

Domain and Range

100

What is the range of the function f(x) = 4x - 12, if the domain is {1, 3, 5, 7}

(-8 , 0 , 8 , 16}

200

find the range

g(x) = -4x + 1, with domain {-5,-1,0,2,10)

(21,  5,  1, -7, -39}

300

Determine if the relation is a function {(a,b) (b,a) (c,c) (e,d) (f,g) (b,h)}

Not a function 

400

if f(x) = 6x - 4 and f(a) = 26 what is the value of a?

a = 5

500

Use the function f(x) = 2x and g(x) = x² + 1 to solve the following

f(3) + g(4)

23

Sequences

100

Tell whether the sequence is arithmetic and find the common difference 

25 , 19 ,13 , 7 

common difference is -6

200

Write the recursive formula for the sequence 

23 , 25 , 47 , 59 

What is the 9th term?

A(n) = A(n-1) + 12

A(9) = 119

300

An arithmetic sequence is represented by the recursive formula 

A(n) = A(n-1) + 15 

If the first term is 42, write the explicit formula 

Find the 10th term. 

A(n) = 42 + (n-1)15

A(10) = 177

400

Write the recursive formula 

A(n) = 76 + (n-1)(10)

Find the first 5 terms.

A(n) = A(n-1) + 10

76 , 86 , 96 , 106 , 116

500

Find the 2nd, 4th, and 11th term of the sequence 

A(n) = 9 + (n-1)(8)

A(2) = 17

A(4) = 33

A(11) = 89