Finding the Domain and Range of a Function (3.8.1)

Question 1

• The domain of a function is the set of all x-values that can be used as inputs for the function.

Answer 1

• The domain of a function is the set of all x-values that can be used as inputs for the function.

Question 2

• The range of a function is the set of all possible y-values, or outputs, for a function.

Answer 2

• The range of a function is the set of all possible y-values, or outputs, for a function.

Question 3

• Values excluded from the domain include values that result in a negative number under a square root sign and values that cause a denominator to equal zero.

Answer 3

• Values excluded from the domain include values that result in a negative number under a square root sign and values that cause a denominator to equal zero.

Question 4

To be judged a function, an equation must have no more than one y-value for every x- value. Graphically, this notion means that if you place a vertical line anywhere on the curve, it will intersect the curve in only one point.
In this case, the domain is all the real numbers because the curve goes on forever to both the right and the left. As a result, every x there is will have some y on the curve. The range is all the real numbers that are used as y-values for a curve. In this example, there will not be any negative y values nor even any positive y values just barely above the x-axis. In this example, the domain is all the values of x, and the range is all the values of y. There are no values that will be missed or excluded in either direction.

Answer 4

To be judged a function, an equation must have no more than one y-value for every x- value. Graphically, this notion means that if you place a vertical line anywhere on the curve, it will intersect the curve in only one point.
In this case, the domain is all the real numbers because the curve goes on forever to both the right and the left. As a result, every x there is will have some y on the curve. The range is all the real numbers that are used as y-values for a curve. In this example, there will not be any negative y values nor even any positive y values just barely above the x-axis. In this example, the domain is all the values of x, and the range is all the values of y. There are no values that will be missed or excluded in either direction.