The ordered pairs in section 1 of this lesson can also be represented in a table. In a table, like the one below, the domain is usually listed in the left column and the range is listed in the right column. You can also refer to the domain as the input values, x, and the range as the output values, y, in a relation or function.

Click in the blank spaces in Table 1 below to reveal the values from the ordered pairs in section 2.

Since a table is just another representation of the ordered pairs, the domain and range are the same.

D: {90, 180, 270, 360}
R: {3.8, 8.0, 12.5, 17.4}

Let’s look at another problem.

The domain of the function f(x) = √4x + 1 is 1 over 4 - 1 4 , 0, 2, 6, and 12. What is the range of the function? Before you answer, copy the table below onto a sheet of paper. Fill in the missing values. Click on the empty spaces to check your answers.

### Conclusion Questions

• What is the range from the table above?

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R = {0, 1, 3, 7}

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When you evaluate each x-value in the function, the result is the output value. These output values are the range.

### Pause and Reflect

Domain and range help connect between the independent and dependent variables of a function. They can also help you make reasonable conclusions about what values are acceptable in each domain and range set.

• Given that the domain and range are both from the set of real numbers, why can’t -2 be in the domain of the function, f(x) = √4x + 1?

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Replacing x is -2 will result in a negative number under the square root. Since you cannot take the square root of a negative number and get a real number, -2 could never be in the domain.

• Given that the domain and range are sets of real numbers, why can’t -2 be in the range of the function, f(x) = √4x + 1?

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Since evaluating the expression with any number less than 1 over 4 - 1 4 would result in a negative number under the square root, you can conclude that any number less than 0 would not be in the range.

### Practice

 Number of sides of a regular polygon Sum of the degress of the interior angles 3 180 4 360 5 540 6 720 7 900 8 1080

1. What is the domain for the table above?

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The domain is the set of values in the left column.

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D: {3, 4, 5, 6, 7, 8}

2. What is the range for the table above?

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The range is the set of values in the right column.

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R: {180, 360, 540, 720, 900, 1080}

3. Based on the independent variable, what is a number that is not in the domain of the table above?

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In this instance, the independent variable is the number of sides of a regular polygon. Think about the number of sides it takes to make a polygon.

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One possible answer is any number less than 3 since a triangle is the polygon with the least number of sides. Another possible answer is any rational number that is not a whole number. For example, 4.5 would not be in the domain since you cannot have a polygon with four and a half sides.
4. Based on the dependent variable, what is a number that is not in the range of the table above?

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The dependent variable represents the sum of the degrees of a regular polygon. Think about what values would not be a reasonable sum.

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One possible answer is any number less than 180. Another possible answer is any number that is not a multiple of 180.