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Relations
Functions
Simple Functions
Composite Functions
Inverse Functions
100

WHAT IS A RELATION?

A relation is a set of ordered pairs that shows a connection or correspondence between elements of two sets.

100

Which of the 4 relations are functions?

One-to-one

Many-to-One

100

If f(x) = 3x - 5, what is f(2)?  

1

100

What does (fg)(x) represent?

The composition of functions f and g, meaning f applied to the output of g. 

The function g is inserted into the function f

100

What is the inverse of a function

A function that when you multiple a function by will result in x

200

How can you determine if a relation is a function?

A relation is a function if for every input (element in the domain), there is exactly one output (element in the range). You can use the vertical line test to check if a graph represents a function. If any vertical line intersects the graph more than once, it is not a function

200

What are the four ways in which a function can be represented?

Ordered pairs

Graph

Table

Mapping Diagram

200

Given g(x) = x2 + 4, find g(-3).

13

200

If f(x) = 2x -4 and g(x) = 3x + 2 Evaluate fg(x)

fg(x) = 6x.

200

If f(x) and g(x) are inverse functions, what is the value of (f o g)(x)?

x

300

What is the difference between domain and range in a relation?

  • Domain: The set of all input values in a relation.
  • Range: The set of all output values in a relation.
300

What is the name of a function where the output is always equal to the input?

Indentity Function

300

If f(x) = 3x - 5, what is the value of x when f(x) = 7?

x= 4

300

If f(x) = 2x + 1 and g(x) = x^2, what is (f o g)(3)?

19

300

Find the inverse of the function f(x) = 2x - 5.

(x+ 2)/ 5

400

What is the inverse of a relation?

The inverse of a relation is formed by switching the x and y coordinates of each ordered pair. It is essentially the reverse of the original relation. If a relation is a function, its inverse may or may not be a function.

400

What is the domain and Range of a function?

The domain is the set of all x values or objects while the Range is all the set of y values Or the image

400

Given f(x) = 2x + 7 , what value of  x is f(x) =0

x= -7/2

400

Given f(x) = 2x +3 / 3x-6, what value for f(x) = 0

x= -3/2

400

If gf(x) = 3x2 - 6 what is (gf)-1 (x)

√((x + 6) / 3).

500

There are four main types of relations:

  • One-to-one: Each element in the domain is paired with exactly one element in the codomain.
  • Many-to-one: Multiple elements in the domain can be paired with the same element in the codomain. 
  • One-to-many: One element in the domain can be paired with multiple elements in the codomain. This type of relation is not considered a function.
  • Many-to-many: Multiple elements in the domain can be paired with multiple elements in the codomain. This type of relation is also not considered a function.
500

What is the vertical line test used for?

To determine if a graph represents a function.

500

Given g(x)= 3x + 6 Evaluate g(0)

g(x) = 6

500

Find gf(x) if f(x) = 2x2 - 4 and g(x) = 4x + 5

gf(x) = 8x2 - 11.

500

If the function f(x) represents the temperature in degrees Fahrenheit, what does the inverse function f^(-1)(x) represent?

The temperature in degrees Celsius