Unit 1: Functions Review

function definition

100

This test can be used to determine if a graph is a function.

VLT or Vertical Line Test

200

A term that describes a set of ordered pairs (x,y)

relation

300

A function occurs when......

x values do NOT repeat

400

Mr. Kirsch says that the relation (0,1), (0,2), (1,3), (3,4) is a function.  Is he correct?  JUSTIFY!

No.  The x value of 0 repeats

500

True or False:  All relations are functions

False.  If an x value is repeating, it is NOT a function

evaluating functions

100

In the equation y=3x+10, the y represents the ______

output

200

In the equation f(x)=-4x-7, the x represents the _____

input

300

f(x) = 5x-12

find f(4)

8

400

f(x) = x² +12

f(x) = 7, find x

61

500

Besides plugging in, there are 3 other ways to evaluate a function.  Name all 3 ways.

1. Table

2. Store 

3. Nsolve

function notation

100

The set of all x values is also called the 

domain

200

the range is another name for the ____ values

y

300

Using INTERVAL NOTATION, write out " x is greater than or equal to -5"

[-5, infinity)

400

Using INEQUALITY NOTATION, write out " x is greater than -4 and less than 5".

-4<x<5

500

Using your calculator, graph the function x²-2x-1. What are the DOMAIN and RANGE of this graph (use interval notation)

domain: (-infinity, infinity)

range: [-4, infinity)

composition of functions

100

In a composition of functions, there will be __ functions to plug into.

2

200

In the composition f(g(x)), plug into the ____ function first.

g

300

f(x)=3x+2

g(x)=5x-4

determine g(f(2))

36

400

f(x)=x²+5

g(x)=2x-3

find f(g(3))

14

500

f(x)=3x+1

g(x)=4x-5

find f(g(x))

3(4x-5)+1

12x-15+1

12x-14

1:1, inverse functions and key features

100

In a 1:1 function, what CANNOT repeat?

BOTH x's and y's CANNOT repeat

200

The INVERSE of (x,y) is 

(y,x)

300

A circle is NOT a 1:1 function.  Tell which test(s) can be used to prove this.

VLT and HLT

400

The x-intercepts of a graph can also be called the ______ or the ______

roots or zeroes

500

A portion of a graph is NEGATIVE if it falls ________ the ___________.

it falls BELOW the X-AXIS