What is the DOMAIN and RANGE for the following equations:

Question

1) y = 3x - 4
2) y = -2x^2 + 2
3) y = x^3
I know how to graph I understand all that but I don'T know how to determine the range and domain, are they looking for number pairs????
Thanks

Answer 1

(1)

The equation is .

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for x and find the corresponding values for y.

x		(x, y)
1
2
3

Draw a coordinate plane.

Plot the coordinate points.

Then sketch the graph, connecting the points with a line.

Since x can be any real number, there is an infinite number of ordered pairs that can be graphed. All of them lie on the line shown.

Notice that every real number is the x - coordinate of some point on the line.

Also, every real number is the y - coordinate of some point on the line.

So, the domain and range are both all real numbers, and the relation is continuous.

Answer 2

(2).

The function is .

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for x and find the corresponding values for y.

x		(x, y )
1
2

To draw the equation follow the steps.

1. Draw a coordinate plane.

2. Plot the points on the coordinate plane.

3.Then sketch the graph, connecting the points with a smooth curve.

Since x can be any real number, there is an infinite number of ordered pairs that can be graphed. All of them lie on the graph shown.

Notice that every real number is the x - coordinate of some point on the graph, so the domain is all real numbers.

But, only real numbers less than or equal to 2 are y - coordinates of points on the graph. So the range is .

Answer 3

(3)

The equation is .

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for x and find the corresponding values for y.

x		(x, y)
0
1
2

Draw a coordinate plane.

Plot the coordinate points.

Then sketch the graph, connecting the points with a line.

Since x can be any real number, there is an infinite number of ordered pairs that can be graphed. All of them lie on the graph.

Notice that every real number is the x - coordinate of some point on the graph.

Also, every real number is the y - coordinate of some point on the graph.

So, the domain and range are both all real numbers.