Question

The graph of the function f(x) = (x +2)(x + 6) is shown below. what is true about the domain and range of this function

Answer 1

Given :

function f(x) = (x +2)(x + 6)

To Solve :

Range & domain of the given function

Solution :

•Given function is f(x) = (x +2)(x + 6)

f(x) = x² + 6x + 2x + 12

f(x) = x² + 8x + 12

•Since it is a polynomial function hence ,it accepts all the real values.

•So , Domain of function f(x) is R

• According to GRAPH

y = x² + 8x + 12

ADDING 4 both sides

y + 4 = x² + 8x + 12 + 4

y + 4 = x² + 8x + 16

y + 4 = ( x +4)²

• It is of the form x² = 4ay

which the equation of parabola

clearly , it is equation of upper parabola with its axis as y axis

•Vertex of parabola is at (-4 , -4) & focus will be at ( 0 , 1/4 )

• Since Vertex is at ( -4 , -4 ) & it is upward parabola

=> min. value of f(x) is -4

=> Range f(x) € [-4, infinity ]

Hence , Domain f(x) € R & Range f(x) € [-4, infinity ]