BUNDLE: Functions and Relations With Lab Activity By, Kindly Pass the Math

Understand Input and Output Identify Functions and Relations Today’s Goals: Graph a Linear Function Use the Vertical Line Test Write a function In Functional Notation By, Kindly Pass the Math

By definition, a FUNCTION is a rule that establishes a relationship between two quantities. These two quantities are called an input and an output; in a function, for each input, there is exactly one output. By, Kindly Pass the Math

A RELATION is ANY set of ordered pairs. A relation can be a function, or it cannot be a function. Let’s take a closer look at this…

This is an example of a RELATION: {(1,3), (2,4), (2,5)} Notice that two of the input values are the number 2. Since a relation is any set of ordered pairs, this is, most assuredly, a relation. However, it is NOT a function. This is because all the inputs (or x values) must be different. As you can see, in this set of ordered pairs all x values are not different; two are the same. By, Kindly Pass the Math

Let’s look at a few more examples: Determine whether or not each of the following sets of ordered pairs is or is not a function: {(-3,3), (0,3), (2,0)} {(2,0), (0,2), (2,2)} {(4,5), (-4,4), (2,3)} {(3,-3), (2,2), (3,3)} By, Kindly Pass the Math

Answers to examples: Determine whether or not each of the following sets of ordered pairs is a function: {(-3,3), (0,3), (2,0)} Yes {(2,0), (0,2), (2,2)} No {(4,5), (-4,4), (2,3)} Yes {(3,-3), (2,2), (3,3)} No By, Kindly Pass the Math

There are many ways to represent a Relation: As a set, using brackets and parentheses With a table With an input/output chart With a graph With an equation using functional notation The domain is the set of all input values, or x values; the range is the set of all output values, or y values By, Kindly Pass the Math

A relation can be shown as a set using brackets and parentheses {(1,2), (0,1), (-1,0)} Is this a function? What is the domain? What is the range? By, Kindly Pass the Math

As a set, using brackets and parentheses: {(1,2), (0,1), (-1,0)} Is this a function? yes What is the domain? Set of all x values: (1, 0, -1) What is the range? Set of all y values: (2,1,0) By, Kindly Pass the Math

As a set, using brackets and parentheses: {(1,-3), (1,1), (-4,0)} Is this a function? What is the domain? What is the range? Try One! By, Kindly Pass the Math

{(1,-3), (1,1), (-4,0)} Set of all x values: (1, 1, -4) As a set, using brackets and parentheses: {(1,-3), (1,1), (-4,0)} Is this a function? No What is the domain? Set of all x values: (1, 1, -4) You really only need to write the duplicating numbers once: (1, -4) What is the range? Set of all y values: (-3,1,0) Check Your answers By, Kindly Pass the Math

A relation can be shown using a table: Input (x) 2 -2 3 Output (y) -5 Is this a function? Name the Domain Name the Range By, Kindly Pass the Math

A relation can be shown using a table: Input (x) 2 -2 3 Output (y) -5 Is this a function? Yes Name the Domain (0, 2, -2, 3) Name the Range (-5, 2, 0) By, Kindly Pass the Math

A relation can be shown using an input/output chart: y x 3 -1 5 -2 4 6 By, Kindly Pass the Math

A relation can be shown using an input/output chart: Yours To try y x 6 1 4 -2 2 -1 3 Is this a function? Name the domain. Name the range. By, Kindly Pass the Math

A relation can be shown using an input/output chart: Answers y x Is this a function? Yes Name the domain. (6, 1, 4, -2) Name the range. (2, -1, 0, 3) 6 1 4 -2 2 -1 3 By, Kindly Pass the Math

A relation can also be shown by plotting the ordered pairs on a coordinate plane: (3,3) (2,1) x (-3, 0) (-1, -1) By, Kindly Pass the Math

Is this a function? Name the domain. Name the range. y (0,1) x (-1, 0) (-1, -1) (2,-2) By, Kindly Pass the Math

Is this a function? No Name the domain. (0, -1, 2) Name the range. (1, 0, -1, -2) y Answers (0,1) x (-1, 0) (-1, -1) (2,-2) By, Kindly Pass the Math

There is a test you can use to determine whether or not a graph of plotted points represents a function; it is called the VERTICAL LINE TEST. Here is how it works: To be a function, no vertical line can intersect the graph of multiple ordered pairs more than once. By, Kindly Pass the Math

No vertical line can intersect the graph of multiple ordered pairs more than once if it is a function. Now, drawing a vertical line through the graph, does it intersect the graph once, or more than once? By, Kindly Pass the Math

No vertical line can intersect the graph of multiple ordered pairs more than once if it is a function. More than once! This is not a function! By, Kindly Pass the Math

Does this represent a function? No vertical line can intersect the graph of multiple ordered pairs more than once if it is a function. Does this represent a function? By, Kindly Pass the Math

No vertical line can intersect the graph of multiple ordered pairs more than once. Does this represent a function? Yes, a vertical line passes through the graph only one time; it passes the vertical line test! By, Kindly Pass the Math

f (x) instead of y in slope-intercept form of an equation. Functional Notation is a convenient way to define a function. To write a function using functional notation, you simply write f (x) instead of y in slope-intercept form of an equation. “f (x)” is read as “f of x” Here is an equation: y = 2x + 1 In functional notation, it is written: f (x) = 2x + 1 Their meanings are the same. By, Kindly Pass the Math

Evaluating a function: Example: Evaluate f (x)=x-3 when x is 2 Therefore, when x is 2, y is -1 By, Kindly Pass the Math

Try this! Any volunteers? f (x)= 2x + 3 when x = 4 By, Kindly Pass the Math

Check your answer! f (x)= 2x + 3 when x = 4 f (x) = 2(4) + 3 By, Kindly Pass the Math

Graphing a Linear Function Graph f (x) = 2x -3 First, re-write it in equation form: y=2x -3 Next, make a table of values (select random values for x), figure out the value of y to make a true statement, then plot the points: X 2 3 -1 y 1 -5 By, Kindly Pass the Math

Graphing a Linear Function Graph f (x) = -2x + 2 Give it a try! Hint: select small values for x, like 1, -1, or 0 X y By, Kindly Pass the Math

Use the model to estimate the distance traveled after 28 days. Monarch butterflies migrate from Northern United States to Mexico, distance of 2000 miles in approximately 40 days. Write a linear function that models the distance traveled by monarch butterflies. Recall that d=rt Use the model to estimate the distance traveled after 28 days. Graph your model and label the point representing the distance traveled after 28 days. By, Kindly Pass the Math

Use the model to estimate the distance traveled after 28 days. Write a linear function that models the distance traveled by monarch butterflies. Recall that d=rt r = 2000/40 = 50 D = 50t Use the model to estimate the distance traveled after 28 days. D = 50 (28) = 1400 miles By, Kindly Pass the Math

Graph your model and label the point that the butterflies will be after 20 days. d=50t 2000 1800 1600 1400 1200 1000 800 600 400 200 5 10 15 20 25 30 35 40 45 By, Kindly Pass the Math

Use the model to estimate the distance traveled after 12 days. Try this! It’s easy!! Monarch butterflies migrate from Northern United States to Mexico, distance of 2000 miles in approximately 50 days. Write a linear function that models the distance traveled by monarch butterflies. Recall that d=rt Use the model to estimate the distance traveled after 12 days. Graph your model and label the point representing the distance traveled after 12 days. By, Kindly Pass the Math

Use the model to estimate the distance traveled after 12 days. Write a linear function that models the distance traveled by monarch butterflies. Recall that d=rt r = 2000/50 = 40 D = 40t Use the model to estimate the distance traveled after 12 days. D = 40 (12) = 480 miles By, Kindly Pass the Math

Graph your model and label the point that the butterflies will be after 12 days. Volunteer To graph This? d=40t 2000 1800 1600 1400 1200 1000 800 600 400 200 5 10 15 20 25 30 35 40 45 By, Kindly Pass the Math

Graph your model and label the point that the butterflies will be after 12 days. This is how Your Graph Should Look… d=40t 2000 1800 1600 1400 1200 1000 800 600 400 200 5 10 15 20 25 30 35 40 45 By, Kindly Pass the Math

Thank You!!! Kindly Pass the Math Thank you for your dedication to children… Thank you for your welcomed encouragement… Thank you for your trust in my TPT product… Butterfly clip art by: jimmiet_Monarch_Butterfly.png And monarch_butterfly_clipart_png_ Mathematical designs by, Kindly Pass the Math Please remember to rate this product and follow my store for future products and freebies. https://www.teacherspayteachers.com/Store/Kindly-Pass-The-Math All rights reserved by Kindly Pass the Math 2016

Math Lab Is it a Function or NOT? By, Kindly Pass the Math By, Kindly Pass the Math

The following activity Functions and Relations. reinforces Functions and Relations. Students may work independently or with a partner, whatever your pleasure! By, Kindly Pass the Math

A pair of die (each a different color) Materials Needed: A pair of die (each a different color) A ruler Graph paper (included in slides) By, Kindly Pass the Math

Directions: Roll a pair of die (each die a different color) five times to complete the chart on the next slide. Let one color die represent the x coordinate and the other color die represent the y coordinate. Write the results of each toss as an ordered pair with x on the left and y on the right (x, y). Record each of the ordered pairs thrown, unless you throw the same pair twice; then, roll again. By, Kindly Pass the Math

Die #1 (x) Die #2 (y) As an Ordered Pair (x, y) Toss #1_________________________________________ Toss #2__________________________________________ #3__________________________________________ #4__________________________________________ #5_________________________________________ By, Kindly Pass the Math

Plot your ordered pairs on the graph provided: x By, Kindly Pass the Math

(this means use brackets { }). Analysis Questions Directions: In the spaces provided below, write (or type) the question in one color, and answer it in another color using full and complete sentences. 1. Write the ordered pairs as a set of ordered pairs (this means use brackets { }). By, Kindly Pass the Math

What is the DOMAIN of your set of ordered pairs What is the DOMAIN of your set of ordered pairs? Write the DOMAIN as a set of numbers. Again, use brackets { }. By, Kindly Pass the Math

Does the domain show that your set of ordered pairs is a function Does the domain show that your set of ordered pairs is a function? What is it that indicates whether or not your relation is a function? Explain. By, Kindly Pass the Math

4. What is the RANGE of your set of ordered pairs 4. What is the RANGE of your set of ordered pairs? Write the RANGE as a set of numbers Again, use brackets { }. By, Kindly Pass the Math

For example, if you rolled (2,6), the inverse would be (6,2). What is the inverse of your relation? Write the inverse as a set of ordered pairs Again, use brackets { }. For example, if you rolled (2,6), the inverse would be (6,2). By, Kindly Pass the Math

Which, if any, of your ordered pairs is a solution to 2x – y = 3 Which, if any, of your ordered pairs is a solution to 2x – y = 3? Test each ordered pair you rolled in this equation. There are an infinite number of possibilities! Yes/no 2( ) - ( ) = 3 (x , y) By, Kindly Pass the Math

Ordered Pair: Unique Equation: a) b) c) d) e) Write a unique linear equation for each of the ordered pairs you rolled.! For example, if you rolled (2,4), you could write 2x + y = 8 or y – x = 2. There are an infinite number of possibilities. First write your ordered pair, and then write your unique equation. Ordered Pair: Unique Equation: a) b) c) d) e) By, Kindly Pass the Math

8. In your own words, describe the difference between a relation and a function. Be neat in your work! Please…! No scribbles or lunch residue smudges! In other words, and I repeat, be neat in your work. I am looking for quality work. By, Kindly Pass the Math

The VERTICAL LINE TEST for a function states that if any vertical line passes through no more than one point of the graphed relation, the relation is a function. Does the vertical line test on the next page indicate that your relation is a function? To find out, plot your ordered pairs, connect them from left to right, and then draw a vertical line through the graph. Does the vertical line pass through the graphed ordered pairs in more than one point? If so, your ordered pairs does not indicate that it is a function. Briefly explain the situation with your set of ordered pairs here; is it a function, or is it not?: By, Kindly Pass the Math

Plot your ordered pairs, connect them from left to right, and then apply the Vertical Line Test: y x By, Kindly Pass the Math

Thank You!!! Kindly Pass the Math Thank you for your dedication to children… Thank you for your welcomed support… Thank you for your trust in my TPT products… This product has been originally written By Kindly Pass the Math Please remember to rate this product and follow my store to receive future products and freebies! https://www.teacherspayteachers.com/Store/Kindly-Pass-The-Math @ all rights reserved by Kindly Pass the Math 2016