Find the domain and range of

Question

f(x)= [8-(x+2)^2]/4 

Answer 1

The function f(x) = [ 8 - (x + 2)²]/4

y = 8/4 - (x + 2)²/4

y = 2 - (x - (-2))²/4

y = -(1/4)[x - (-2)]² + 2

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

a = -1/4, h = - 2, k = 2

a is negative number the parabola opens downward and has maximum value.

Vertex is the maximum point of parabola .

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

Domain of function is all real numbers.

In the maximum point y = 2,  so the graph of parabola cannot be upper than 2.

Thus the range of function y ≤ 2.