domain and range y=x^2-4

Question

The domain and range

Answer 1

Given function is f(x) = y = x^2-4

For x = 0

y = 0^2-4 = -4

Forx = 1

y = 1^2-4 = -3

For x = 2

y = 2^2-4 = 0

For x = 3

y = 3^2-4 = 5

For x = -1

y = (-1)^2-4 = -3

For x = -2

y = (-2)^2-4 = 0

For x = -3

y = (-3)^2-4 = 5

x value half coordinate pair and y value is half coordinate pair.

If x = 0,1,2,3,-1,-2,-3 respectively substitute the x values in given function the set of coordinate pair is be

-4,-3,0,5,-3,0,5

we know that x values is domain of the function and y values is range of the function.

Domain set is {0,1,2,3,-1,-2,-3}

Range set is {-4,-3,0,5,-3,0,5}

Answer 2

y  = x ² - 4

Compare it to standard form of parabola y = ax ² + bx + c.

a  = 1 , b  = 0, c  = -4.

We know that parabola like a curve.

a  is positive , so the parabola opens upward.

The parabola giving us all real numbers is the domain.

To find the range

axis of symmetry x = -b /2a

x  = 0

Substitute the x value in y = x ² - 4

y  = 0 - 4

Vertex of the parabola (x,y ) = (0, -4)

Vertex of parabola gives us minimum y  value that corresponds to find the range.

In the minimum point y = -4,so the graph of parabola cannot be lower than -4.

The range Contains all real numbers greter than or equal to -4.

Domain is all real numbers.

Range .