Quadratic function??? Confused.?

Question

F(x)=(x-1)^2-5 ~~~~find domain & range? How???

Answer 1

Domain :

F(x)= (x-1)² - 5

The domain are all x values that has images.

 we do not have any restrictions on the values of x .

==> Therefore, the domain is all real values :(-∞ , ∞).

 

 

Answer 2

Range :

F(x)= (x-1)² - 5

An algebraic method to find the range

(x - 1)² ≥ 0

(x - 1)² - 5 ≥ -5

F(x) ≥ -5

Therefore the range of the function  F(x) : [-5 , ∞).

 

 

Answer 3

The function f (x ) = (x - 1)² - 5

y = (x - 1)² - 5

The above function represents a parabola vertex form  y = a (x - h )²+ k .

Where vertex of parabola (h ,k )

 a  = 1 , h  = 1 and k  = - 5.

a  is positive number the parabola opens up and has minimum value.

When the parabola opens up it has a minimum point which is the vertex of parabola (1, - 5)

We know that domain of the function is all possible x  values and range is all posible y  values.

 parabola domain x  =  all real numbers.

In the minimum point y  = - 5  so the graph of parabola cannot be lower than - 5.

Thus the range of function y  ≥ - 5.

Domain of function is all real numbers.

Range of the function is  {y ∈ R : y  ≥ - 5}.