What is the domain and range of this function in interval notation??

Question

x^2-2x-15

Answer 1

 

Since x can be any real number the domain is (-infinity,infinity)

 

To find the range we need to find the vertex of the parabola which is at (-b/2a , y)

-b/2a would be 2/2 = 1 ... so find the y value at x = 1

1² - 2(1) - 15 = 1-17 = -16

So the vertex is at (1,-16)

Since the parabola opens upward from that point the minimum value of the range is y = -16

The range would include the point -16 so it is actually

R = [-16,infinity)

Answer 2

We have here a graph that represents a polynomial.  The domain of a graphed polynomial is all real numbers.

 

(-∞, ∞)

 

 

The range is the maximum or minimum y-value that the graph will reach.  We can find this by using the vertex form of the function, since we have a positive parabola.

 

y = a(x - h)² + k

 

where

 

vertex is (h, k).

 

y = (x² - 2x + 1) - 16

 

y = (x - 1)(x - 1) - 16

y = (x - 1)² - 16

 

The vertex is (1, -16).

 

The vertex is also the point where the graph turn direction.  This is a minimum because we have a positive parabola.

 

The range is

 

(-16, ∞)