Lesson Notes 3.1 and 3.2 Intro to Functions

Coordinate Plans

The Coordinate Plane is a two-dimension plane that is formed when the x-axis (running horizontally - left/right) intersects with the y-axis (running vertically - up/down).

Origin

The x-axis and y-axis intersect at a point called the ORIGIN.

Each point on the coordinate plane can be represented by an ordered pair (x.y) which state the coordinate location of each point. The origin is located at (0,0).

Multiple Choice

The coordinate plane is divided by a horizontal number line called ______________

• x-axis

• y-axis

• origin

• quadrant

Multiple Choice

The coordinate plane is divided by a vertical number line called ______________

• x-axis

• y-axis

• origin

• quadrant

Multiple Choice

The coordinates for the origin in the coordinate plane are________

• (x,y)

• (0,0)

• (1,1)

• (2,8)

Quadrants

This intersection also creates four quadrants where points can be plotted. 

To name quadrants, begin at the top right where all the positive values of both x and y are located.

This is Quadrant I. To name the others, move in a counterclockwise rotation.

Multiple Choice

In which quadrant is point N?

• Quadrant 1

• Quadrant 2

• Quadrant 3

• Quadrant 4

Multiple Choice

In which quadrant is point P?

• Quadrant 1

• Quadrant 2

• Quadrant 3

• Quadrant 4

Plotting Points

Although there are two coordinates given for an ordered pair, it is a series of these two movements that result in one plotted point.

(x, y)

First follow the x to move left/right,

Then follow the y to move up/down.

Multiple Choice

What is the coordinate for point C?

• (2,4)

• (4,2)

• (2,5)

• (-2,4)

Multiple Choice

If my coordinates are (3, 4) what is my y?

• 3

• 4

• There is no y

Multiple Choice

If I want to plot point (4,9), I will go up 4 and over 9

• True

• False

Multiple Choice

What is the coordinate for point A?

• (2,2)

• (2,-2)

• (-2,2)

• (-2,-2)

Multiple Choice

What is the coordinate for point D?

• (2,2)

• (2,-2)

• (-2,2)

• (-2,-2)

Multiple Choice

State the domain of the given relation:

• {2, 3, 7}
• {1, 4}
• {1, 2, 3, 4, 7}

Multiple Choice

State the range of the given relation.

• {2, 3, 7}
• {1, 4}
• {1, 2, 3, 4, 7}

Multiple Choice

What is the domain and range of the relation represented by the ordered pairs {(2, -3), (-1, 4), (0, 2), (2, 4), (5, -1)}?

• Domain: {2, -1, 0, 5}; Range: {-3, 4, 2, -1}

• Domain: {-3, -1, 0, 2, 5}; Range: {4, 2, -1}

• Domain: {2, -1, 0, 4, 5}; Range: {-3, 4, 2, -1}

• Domain: {-3, 4, 2, -1, 5}; Range: {2, 0, 4, 5}

Multiple Choice

What is the definition of function?

• Has inputs and outputs
• Every input has only ONE output
• Inputs have different outputs every time
• x-values and y-values

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

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function 

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this graph a function or not a function?

• Function
• Not a Function

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

Multiple Choice

Is this table a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function

Multiple Choice

Which graph does NOT pass the vertical line test?

• Graph 1
• Graph 2
• Graph 3
• Graph 4

Multiple Choice

Is this graph a function or not a function? 

• Function 
• Not a Function 

Multiple Choice

Does the table represent a function?

• Yes, there  is a repeated x-value. 
• No, there aren't any repeated y-values. 
• Yes, there are repeated y-values. 
• No, there is a repeated x-value. 

Multiple Choice

All of the x values or inputs are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

All of the y values or outputs are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

Multiple Choice

Which ordered pair could you add to the following list of points to create a function?  (3, 5) (4, 9) (2, 5) 

• (3, 7)
• (4, 1) 
• (1, 9)
• (2, 6)

Multiple Choice

Which of the following best describes the domain of a relation?

• The set of all y-values in the relation

• The set of all x-values in the relation

• The set of all ordered pairs in the relation

• The set of all points in the first quadrant

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)
• (3,4) (4,-3) (7,4) (3, 8)
• (6,-5) (7, -3) (8, -1) (9, 1)
• (2, -2) (5, 9) (5, -7) (1, 4)

Multiple Choice

Is this graph a function or not a function? 

• Function 
• Not a Function

Multiple Choice

Which of the following relations is NOT a function?

• {(5, -2), (3, -5), (2, -5), (0, -2), (-1, -3)}

• {(-2, 3), (0, 1), (2, -4), (3, -1), (2, 4)}

• {(-4, -1), (-3, -1), (-2, -3), (1, 0), (3, 2)}

• {(1, -5), (2, -3), (3, -1), (4, 0), (5, 2)}

Multiple Choice

How do we read Domain of Continuous Data?

• Left to Right

• Bottom to Top

Multiple Choice

How do we read Range of Continuous Data?

• Left to Right

• Bottom to Top

What is the domain for the graph shown above?

Multiple Choice

What is the domain for the graph shown in the slide before?

• $$-5\le x<5$$

• $$-5\le y\le5$$

• $$-5\le x\le5$$

• $$-5\le y\le7$$

What is the range for the graph shown above?

Multiple Choice

What is the range for the graph shown in the slide before?

• $$-6\le x\le5$$

• $$-5\le y\le5$$

• $$-6\le y\le5$$

• $$-5\le x\le5$$

Multiple Choice

Is this graph Discrete or Continuous?

• Discrete
• Continuous

Multiple Choice

State the range of the graphed function.

• -2 ≤ 𝒙 ≤ 4
• -1 ≤ 𝒚 ≤ 3
• -1 ≤ 𝒙 ≤ 3
• -2 ≤ 𝒚 ≤ 4

Multiple Choice

State the domain of the graphed function.

• -1 ≤ 𝒙 ≤ 3
• -2 ≤ 𝒚 ≤ 4
• -2 ≤ 𝒙 ≤ 4
• -1 ≤ 𝒚 ≤ 3

Multiple Choice

What is the range of this function?

• -4 ≤ y ≤ 5
• -1 ≤ x ≤ 3
• All Real Numbers
• y ≥ -4

Multiple Choice

What is the domain & range for this function?

• 
  

  $$D:\ \left\{0\le x\le8\right\}$$ $$R:\left\{0\le y\le8\right\}$$
  

• $$D:\left\{All\ Real\ Numbers\right\}$$ $$R:\left\{All\ Real\ Numbers\right\}$$

• $$D:\left\{-4\le x\le3\right\}\$$ $$R:\left\{1\le y\le7\right\}$$

Multiple Choice

Which is the correct domain and range for this function?

• $$D:\left\{0\le x\le8\right\}$$ $$R:\left\{0\le y\le8\right\}$$

• $$D:\left\{All\ Real\ Numbers\right\}$$ $$R:\left\{0\le y\le8\right\}$$

• $$D:\left\{All\ Real\ Numbers\right\}$$ $$R:\left\{All\ Real\ Numbers\right\}$$

Multiple Choice

What is the correct domain and range for this function?

• $$D:\left\{All\ Real\ Numbers\right\}$$ $$R:\left\{All\ Real\ Numbers\right\}$$

• $$D:\ \left\{-4\le x\le3\right\}$$ $$R:\left\{1\le y\le7\right\}$$

• $$D:\left\{1\le x\le7\right\}$$ $$R:\left\{All\ Real\ Numbers\right\}$$

Multiple Choice

What is the domain and range for this function?

• $$D:\left\{All\ Real\ Numbers\right\}$$ $$R:\left\{All\ Real\ Numbers\right\}$$

• $$D:\left\{-4\le x\le3\right\}$$ $$R:\left\{1\le y\le7\right\}$$

• $$D:\left\{All\ Real\ Numbers\right\}$$ $$R:\left\{1\le y\le7\right\}$$

Multiple Choice

What is the domain & range for this function?

• 
  

  $$D:\ \left\{0\le x\le8\right\}$$ $$R:\left\{0\le y\le8\right\}$$
  

• $$D:\left\{All\ Real\ Numbers\right\}$$ $$R:\left\{All\ Real\ Numbers\right\}$$

• $$D:\left\{-4\le x\le3\right\}\$$ $$R:\left\{1\le y\le7\right\}$$

Multiple Choice

State the range of the graphed relation.

• -1 ≤ 𝒙 ≤ 3
• -3 ≤ 𝒚 ≤ 3
• {-1, 1, 2, 3}
• {-3, -2, -1, 1, 3}

Multiple Choice

State the domain of the graphed relation.

• -1 ≤ 𝒙 ≤ 3
• {-3, -2, -1, 1, 3}
• -3 ≤ 𝒚 ≤ 3
• {-1, 1, 2, 3}

Multiple Choice

When is the graph increasing?

• 4am - 4pm
• 4am - 12pm
• 12pm - 4pm
• 4pm - 8pm

Multiple Choice

When is the graph decreasing?

• 4pm - 8pm
• 4pm - 8am
• 12pm - 4pm
• 8am - 12pm

Multiple Choice

When is the graph non-linear?

• 4am-8am
• 8am-12pm
• Never
• 4pm-8pm

Multiple Choice

When is the graph increasing?

• 0-10
• 10-40
• 40-60

Multiple Choice

When is the graph decreasing?

• 40 - 60
• 0-10
• 10-40

Multiple Choice

What height is the plane at for most of the flight?

• 12,000
• 0
• 4000
• 8000

Multiple Choice

How many minutes did Justin travel at 6 mph?

• 20
• 10
• 30
• 0

Multiple Choice

How fast was Justin riding the last 20 minutes of his trip?

• 9 mph
• 6 mph
• 50 mph
• 12 mph

Multiple Choice

How long was Justin's trip?

• 70 min
• 50 min
• 12 min
• 60 min

Multiple Choice

What was Justin's max speed?

• 12 mph
• 70 mph
• 10 mph
• 15 mph

Open Ended

Describe a real world situation that would create this graph. Include labels on the x- and y-axis on the graph.

Multiple Choice

Multiple Choice

Multiple Choice