Math: Domain, Range, and Graphs of Functions Worksheet

Question 1

Find the domain and range of the function y = 2x + 5.

Accepted Answer

The domain is all real numbers because any real value of x can be substituted into the equation. The range is all real numbers because the linear function can produce any real y-value.

Question 2

Find the domain of the function y = 1 / (x - 4).

Accepted Answer

The domain is all real numbers except x = 4 because division by zero is undefined.

Question 3

Find the domain of the function y = square root of (x + 7).

Accepted Answer

The domain is x greater than or equal to -7 because the expression inside a square root must be nonnegative.

Question 4

Find the range of the function y = x^2 - 9.

Accepted Answer

The range is y greater than or equal to -9 because x^2 is always at least 0, so the smallest value of y occurs at x = 0 and is -9.

Question 5

A function has the set of ordered pairs {(1, 3), (2, 5), (4, 5), (7, -1)}. State the domain and range.

Accepted Answer

The domain is {1, 2, 4, 7} because those are the x-values. The range is {-1, 3, 5} because those are the y-values, with no repeats listed.

Question 6

The table below shows a function: x-values: -2, 0, 3, 5 and y-values: 4, 1, 4, 9. State the domain and range.

Accepted Answer

The domain is {-2, 0, 3, 5}. The range is {1, 4, 9} because 4 is only listed once in the set of outputs.

Question 7

Determine whether the relation {(0, 2), (1, 4), (1, 5), (3, 7)} is a function. Explain your answer.

Accepted Answer

This relation is not a function because the input x = 1 is paired with two different outputs, 4 and 5.

Question 8

Find the domain of the function y = square root of (5 - x).

Accepted Answer

The domain is x less than or equal to 5 because the expression inside the square root must be nonnegative, so 5 - x must be at least 0.

Question 9

Find the range of the function y = absolute value of x + 2.

Accepted Answer

The range is y greater than or equal to 2 because absolute value outputs are always nonnegative, and adding 2 shifts the minimum value up to 2.

Question 10

A graph is a parabola opening upward with vertex at (3, -4). State the domain and range.

Accepted Answer

The domain is all real numbers because the parabola extends left and right without end. The range is y greater than or equal to -4 because the vertex gives the minimum y-value.

Question 11

A graph is a horizontal line at y = -6. State the domain and range.

Accepted Answer

The domain is all real numbers because the line extends forever to the left and right. The range is {-6} because every point on the graph has y-value -6.

Question 12

Find the domain of the function y = (x + 1) / (x^2 - 9).

Accepted Answer

The domain is all real numbers except x = -3 and x = 3 because those values make the denominator equal to zero.

Question 13

Find the range of the function y = -x^2 + 1.

Accepted Answer

The range is y less than or equal to 1 because the parabola opens downward and has a maximum value of 1 at x = 0.

Question 14

A graph begins at the point (2, 1) and continues to the right and upward like a square root graph. State the domain and range.

Accepted Answer

The domain is x greater than or equal to 2 because the graph starts at x = 2 and moves right. The range is y greater than or equal to 1 because the graph starts at y = 1 and moves upward.

Question 15

Write a possible function that has domain x greater than or equal to 0 and range y greater than or equal to -5.

Accepted Answer

One possible function is y = square root of x - 5. Its domain is x greater than or equal to 0 because x is inside a square root, and its range is y greater than or equal to -5 because the square root output starts at 0 and is shifted down 5 units.

Math: Domain, Range, and Graphs of Functions

Math: Domain, Range, and Graphs of Functions

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