what is the domain and range of the linear and quadratic equation?

Question

Linear : Y=5X+7

 

Quadratic : X²-4X-5

Answer 1

For any linear function the domain and range are always all real numbers (-∞,∞).  

 

For a quadratic the domain is always all real numbers.  

 

To find the range of a quadratic you must find the vertex, which is located at x = -b/2a for a quadratic in standard form ax^2 + bx + c.  

 

In this case the vertex is located at x = 4/(2*1) = 2

 

The value of the quadratic when x = 2 is 

 

2^2 -4*2 - 5 = 4 - 8 - 5 = -9 

 

a is positive so the quadratic opens upward, therefore the vertex is a minimum value, and the quadratic can take any value greater than or equal to the minimum.  

 

So the range is y>= -9  or  (-9,∞)