Unit 1

Question 1

Give three examples of functions

Answer 1

Y=x2
Y=x
Y=sinX

Question 2

Give three examples of non-functions

Answer 2

y2=x2
x2+y2=r2
x=y2

Question 3

Define function

Answer 3

there exists only one y-value for each and every x- value.

it must pass the vertical line test.

Question 4

Define relation

Answer 4

a function and a non- function are still called relations because a relationship still exists between x and y.

Question 5

Define domain

Answer 5

where all the x’s live on a graph.

notation: D: {x|xcR}

Question 6

Define range

Answer 6

where the y’s live on the graph.

notation: R: {y|ycR}

Question 7

What are the 6 ways to represent a function?

Answer 7

1. in words
2. table of values
3. a set of ordered pairs
4. a mapping diagram
5. a graph
6. an equation

Question 8

What is function notation?

Answer 8

it is another way to represent the dependent and independent variables.

Question 9

Independent is ____

Dependent is ____

Answer 9

Independent is x

Dependent is y

Question 10

What are the parent functions?

Answer 10

They are the functions without any transformations

Question 11

What is a family of functions?

Answer 11

a collection of functions that share common characteristics or properties.

Question 12

What are the 5 functions?

Answer 12

Linear function, quadratic function, square root function, reciprocal function, absolute value

Question 13

Linear relations

Answer 13

Parent function: f(x)= x

• a straight line through the origin
• as x goes from negative infinity to positive infinity, the graph extends from quadrant 3 to quadrant 1
• slope= 1
• the line divides the plane in have diagonally.
• D: {x|xcR}
• R: {y|ycR}
• x-intercepts: x=0
• y-intercepts: y=0
• Asymptotes: none

Question 14

Quadratic Functions

Answer 14

Parent function: f(x)= x2

• non-linear
• min at the vertex
• vertex is at (0,0)
• the axis of symmetry: x=0
• graph only in quadrants 1 and 2
• D: {x|xcR}
• R: {y|y greater or equal to 0, ycR}
• Asymptotes: none

Question 15

Square Root

Answer 15

• half a parabola but lying down
• stays in quadrant 1
• increases in height as x approaches infinity
• D: {x|x greater to or equal to 0, xcR}
• R: {y|y greater to or equal to 0, ycR}
• x-intercept: x=0
• y-intercept: y=0
• Asymptotes: none

Question 16

Reciprocal Function

Answer 16

• 0 does not exist
• 2 branches
• D: {x|x does not equal 0, xcR}
• R: {y|y does not equal 0, xcR}
• x-intercept: does not exist
• y-intercept: y= does not exist
• Asymptotes: 2

Question 17

Absolute Value Function

Answer 17

• this is a function that takes in any x-value and spits out positive x-value.
• D: {x|xcR}
• R: {y|y greater to or equal to 0, xcR}
• x-intercept: x=0
• y-intercept: y=0
• Asymptotes: none

Question 18

What are asymptotes?

Answer 18

a line that continually approaches a given curve but does not meet it at any finite distance