Y=x^2-2x-3 Graph each relation

Question

and state its domain and range? 

 

Answer 1

The function is y = x² - 2x - 3.

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	y = x2 - 2x - 3	(x, y )
- 2	y = (- 2)2 - 2(- 2) - 3 = 4 + 4 - 3 = 8 - 3 = 5	(- 2, 5)
- 1	y = (- 1)2 - 2(- 1) - 3 = 1 + 2 - 3 = 3 - 3 = 0	(- 1, 0)
0	y = (0)2 - 2(0) - 3 = 0 - 0 - 3 = 0 - 3 = - 3	(0, - 3)
1	y = (1)2 - 2(1) - 3 = 1 - 2 - 3 = 1 - 5 = - 4	(1, - 4)
2	y = (2)2 - 2(2) - 3 = 4 - 4 - 3 = 4 - 7 = - 3	(2, - 3)
3	y = (3)2 - 2(3) - 3 = 9 - 6 - 3 = 9 - 9 = 0	(3, 0)
4	y = (4)2 - 2(4) - 3 = 16 - 8 - 3 = 16 - 11 = 5	(4, 5)

To draw the equation y = x² - 2x - 3 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.

Graph :

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 greater than or equal to - 4 are y - coordinates of points on the graph. So the range is {y ∈ R : y ≥ - 4 }.