Unit 1: Functions and Relations

Question 1

Relation (U1T1)

Answer 1

A set of input and output values that are represented in ordered pairs.

Question 2

Function (U1T1)

Answer 2

A relation where every x-value only has one y value, the x values dont repeat, and each input has one output.

Question 3

One to One Functions, injection (U1T1)

Answer 3

an injective function which is when different inputs produce different outputs.

Question 4

Horizontal Line Test (U1T1)

Answer 4

So far in this Unit we use it to test if something is a one to one function. It is not a one to one function if the horizontal line goes through the function more than once.

Question 5

onto function (U1T1)

Answer 5

A surjective function that where each input has an output

Question 6

Bijective functions (U1T1)

Answer 6

A function that is both one to one and onto. They are also invertible.

Question 7

Domain (U1T2)

Answer 7

input values, x-values, independent variables

Question 8

Range (U1T2)

Answer 8

Output values, y- values, dependent variables

Question 9

Functional Notation (U1T3)

Answer 9

f(x) pronounced “f of x”
can use any letter like g(x) or h(x).
The f(x) notation is another way to represent the y value.

Question 10

Inverse function (U1T4)

Answer 10

A function is this if its one to one and passes the horizontal line test
Can be represented as y= f-1(x).
you can see it as “undoing” the work of the original function”
In this type of function the x and y coordinates switch places which means that the domain and range are switching places.

Question 11

Functions only have an inverse function if they are… (U1T4)

Answer 11

One to One Functions

Question 12

For functions that are not on to one you would (U1T4)

Answer 12

fix the function so that the inverse is also a function by restricting the domain.

Question 13

Average rate of change (U1T5)

Answer 13

the rate that the output is changing compared to the rate of the input
It helps to quantify how fast a function changes on average over a certain domain interval.
For a function over the domain interval “a is less than or equal to x which is less than or equal to b” by the change in the output/ change in the input

Question 14

The change in function is different from the the average rate of change because… (U1T5)

Answer 14

the average rate of change just finds the values between different intervals of the output

Question 15

x intercepts are also known as (U1T6)

Answer 15

the roots or zeroes of a polynomial

Question 16

Hole (U1T7)

Answer 16

Known as a point or removable discontinuity. That means that a single point in the graph isn’t there. It appears like and is supposed to be drawn as a hole in the graph.

Question 17

Asymptote (U1T7)

Answer 17

known as an infinite discontinuity. This is because there is an invisible vertical line function which it will never touch or cross over.

Question 18

An “error”

Answer 18

in a function graph on a calculator can either be called a hole or any asymptote.

Question 19

Vertical Shifting

Answer 19

function f(x)+k shifts up the function up by absolute “k” units for k>0 and down absolute value of “k” for k>0 and right absolute k units for k>0

Question 20

horizontal shifting

Answer 20

function f(x+k) shifts function left absolute value of “k” units for k>0 and right the absolute value of “k” units for k<0.