Dependent Independent Input Discrete. X Y Output Continuous

Transcription

1 Domain and Range Review Vocabulary Words Dependent Independent Input Discrete X Y Output Continuous Domain is all the values. It is the variable. It is also the of the function. Range is all the values. It is the variable. It is also the of the function. There are many different ways that you will see domain and range written. Let s review some of the ways we ve seen discrete functions represented. A discrete function is one where the points are not connected to each other. If you graphed either of the functions below, it would just be a bunch of points. X Y The type of function you have will help you decide how to write the domain and range.

2 If your function is represented as a list of ordered pairs, a table, or a map, the best way to list your domain and range is using { }. Example 1: Write the domain and range for the following function: (0, 2) (1, -5) (2, 8) (3, 10) Domain: {0, 1, 2, 3} Range: {-5, 2, 8, 10} Look back at the mapping on the previous page and write down the domain and range for that function. D: R: Since these functions are all discrete (they are just specific points, not continuous lines) we have to list the values for x and y. A continuous function is one that can be graphed as a smooth line or curve. When the function is a line, we can t list values because we would have to list every single decimal an impossible thing to do! We need to use a different notation. Look at the graph to the left. See how it is a line? It also has two endpoints: one is at (-7, -3), and the other is at (4, 7). Our domain includes all the values from -7 to 4, and the range includes all the values from -3 to 7. But how do we write that? And how do the endpoints change things?

3 The domain can be written as: D: x The x values are between the numbers, so that s where the x goes. In the blanks, put the smallest x value and the largest x value. Because the endpoints of our graph are included (they are filled in circles), we use the symbol to show that they are valid numbers in the domain. Try writing the range: R: y Look at the graph to the right. What do you notice that s different from the previous graph? What symbols do you think we should use when writing the domain and range of this graph? Remember from graphing inequalities an open circle goes with the < or > sign, and a closed circle goes with the or sign. Now write the domain and range for this function. Make sure you use the correct sign at the correct end!: D: R: Remember domain and range must always go from smallest to largest when you have two endpoints.

4 Another type of graph you may see looks like this: What do the arrows on the ends of the graph mean? Is this a discrete or continuous graph? Since the graph goes on forever at either end, it will cover all x values. We write this domain as x = all real numbers. You can use a capital R with an extra thick vertical line. Some people write a domain like this as D: - < x < The range is a little different, because our graph has a maximum point but no minimum. Our range is all numbers less than or equal to 4. R: y 4 Now try one on your own: D: R:

5 Domain and Range Review Answer Key Vocabulary Words Dependent Independent Input Discrete X Y Output Continuous Domain is all the x values. It is the independent variable. It is also the input of the function. Range is all the y values. It is the dependent variable. It is also the output of the function. There are many different ways that you will see domain and range written. Let s review some of the ways we ve seen discrete functions represented. A discrete function is one where the points are not connected to each other. If you graphed either of the functions below, it would just be a bunch of points. X Y The type of function you have will help you decide how to write the domain and range.

6 If your function is represented as a list of ordered pairs, a table, or a map, the best way to list your domain and range is using { }. Example 1: Write the domain and range for the following function: (0, 2) (1, -5) (2, 8) (3, 10) Domain: {0, 1, 2, 3} Range: {-5, 2, 8, 10} Look back at the mapping on the previous page and write down the domain and range for that function. D: {0, 1, 3, 9} R: {-5, 4, 8, 14} Since these functions are all discrete (they are just specific points, not continuous lines) we have to list the values for x and y. A continuous function is one that can be graphed as a smooth line or curve. When the function is a line, we can t list values because we would have to list every single decimal an impossible thing to do! We need to use a different notation. Look at the graph to the left. See how it is a line? It also has two endpoints: one is at (-7, -3), and the other is at (4, 7). Our domain includes all the values from -7 to 4, and the range includes all the values from -3 to 7. But how do we write that? And how do the endpoints change things?

7 The domain can be written as: D: -7 x 4 The x values are between the numbers, so that s where the x goes. In the blanks, put the smallest x value and the largest x value. Because the endpoints of our graph are included (they are filled in circles), we use the symbol to show that they are valid numbers in the domain. Try writing the range: R: -3 y 7 Look at the graph to the right. What do you notice that s different from the previous graph? Has an open circle endpoint. What symbols do you think we should use when writing the domain and range of this graph? Remember from graphing inequalities an open circle goes with the < or > sign, and a closed circle goes with the or sign. Use a closed circle for start of domain and end of range; open circle for start of range and end of domain. Now write the domain and range for this function. Make sure you use the correct sign at the correct end!: D: -6 x < 6 R: -6 < y 4 Remember domain and range must always go from smallest to largest when you have two endpoints.

8 Another type of graph you may see looks like this: What do the arrows on the ends of the graph mean? Line continues forever in that direction. Is this a discrete or continuous graph? Continuous. Since the graph goes on forever at either end, it will cover all x values. We write this domain as x = all real numbers. You can use a capital R with an extra thick vertical line. Some people write a domain like this as D: - < x < The range is a little different, because our graph has a maximum point but no minimum. Our range is all numbers less than or equal to 4. R: y 4 Now try one on your own: D: -6 < x < 7 R: 2 y < 8