Function Introduction

Relations and Functions

by Jesus Molina

What are functions?

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Multiple Choice

Determine if the relation is a function

• Not a function, each input has more than one output

• Yes it is a function, because each input has exactly on output

• Not a function, input is equal to output

• Yes it is a function, -1/2 is a fraction of 2

Multiple Choice

Does the graph represent a function?

• Yes, because the vertical line test shows there are no repeating input values

• No, because the vertical line test shows there are repeating input values

Multiple Select

Which among the following is a function?

• All of the above

What is Domain and Range?​

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​Examples of Domain and Range with graph and algebraic function

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​Next example...

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​Last example

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​Things to notice...

​On the three previous examples you are able to see the following three components:

​1. The algebraic representation on the left ex. 1/x

​2. A table of values with you independent input on the left "x" and your dependent value on the right "y"

​3. The graphical representation "the picture" of the function covering points from both sides of "0" meaning the immediate positive and negative values around the zero "0"

Multiple Choice

What is the domain of a relation?

• the set of all x-values

• the set of all y-values

Multiple Choice

Which is the set of all y-values or the outputs?

• Domain

• Range

• Relation

• Function

Multiple Choice

What is the range of the mapping?

• {1, 2, 4}

• {0, 1, 2, 3}

• {0, 3}

• {1, 4}

Multiple Choice

What is the domain of the relation shown in the table?

• {12}

• {6, 18}

• {3, 9, 15, 16}

• {13}

​Analyzing the Parent Functions

​Each parent function, as in the "basic" beginning function before any kind of transformation of dilation, has seven key attributes that makes them unique:

​1. Their individual algebraic representation

2. The graph​

​3. Their Domain and Range

​4. Their x and y intercepts

​5. Possible Symmetries

​6. Asymptotic Behavior

​7. Maximum and Minimum values.

​Exmaples of the parent functions covered during this class

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Examples part 2...

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​Examples Part 3...

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Examples part 4...

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​So...

​There are a couple of ways to write domain and range:

​1. Sentence form i.e. All real numbers

​2. Symbolic form {x:}

​3. Inequalities 0<x<5

​4. Brackets and paranthesis (0,9]

​5. Combinations (0,2) u (3,9)

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​We will further explore each method as we progress in the class.

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​Now, let's check for understanding

Multiple Choice

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

• D: {1, -3, -4,}
  R: {0, 1, 2, -4}
• D: {-4, 0, 1, 2}
  R:{-4, -3, 1}
• D: {0, 1, 2, 3, 4}
  R:{1, -3, -4}
• D: {0, 1, 2, -4}
  R: {1, -3, -4, 1}

Multiple Choice

Does the graph represent a function?

• Yes, because the vertical line test shows there are no repeating input values
• No, because the vertical line test shows there are repeating input values

Multiple Choice

What is the domain of the function?

• x>3 
• x≥-3
• y≤4
• y<4

Multiple Choice

What is the range of the graph?

• -7 ≤ x < 5
• -3 ≤ x < 1
• -3 ≤ y < 1
• -7 ≤ y < 5

​Lets stop for a second because this is a good example.

​The circle here is a great example of "part of" but "not included" because you "need it" as a place holder like "it's around here but not here." So, to describe the number of the circle you would use < or > and to describe the number with the dot you would use ≥ or ≤

Multiple Choice

What is the Domain of this linear function?

• -3 < x ≤ 5
• x = -1
• 5 < x ≤ -3
• -2 < x ≤ 6

Multiple Choice

What is the RANGE of this graph?

• y < -3

• y ≤ -3

• y > 1

• y ≥ 1

Multiple Choice

What is the range?

• {-2,2,5}
• {1,3,5,6}
• all real numbers 
• -2<y<5

​So what happens when we apply functions to real life situations?

​Let's try so more graphs and situations with restrictions.

Multiple Choice

What is the domain of the graph?

• [-3, 3]

• (3, -3]

• (-3, 3)

• (2, 10]

Multiple Choice

A holiday church's meal costs $12.50 a person plus a delivery fee of $30. The equation is: f(x)=30+12.5x, where x is the number of hungry people. If there are 15 people in the church, what is the domain?

• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

• 0, 42.50, 55, 67.50, 80, 92.50, 105, 117.50, ....

• None of the above.

Multiple Choice

Leslie's car travels about 25 miles per gallon of gas. Her car needs 14 gallons of gas to be full. What is a reasonable domain?

• $$x\ge25$$

• $$0\le y\le14$$

• $$x\le14$$

• $$0\le x\le14$$

Multiple Choice

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. The equation: C=2h+15. If Frank has $33 to spend, what is the domain of the situation?

• 0 < x < 9

• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

• 15, 17, 19, 21, 23, 25, 27, 29, 31, 33

• 0 < y < 33

​Alright! we will further discuss the topic of "restrictions" tomorrow when we work on inverse functions.

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Make sure to complete the assignment on Step 3.​