Question

Which of the following accurately shows the range of the function defined below?

Answer 1

Answer:

[2, positive infinity)

Step-by-step explanation:

the range is the interval of possible y-values or f(x) values.

for x<0 y is always and only 3.

for x between 0 and 2, y = x² + 2.

it clearly increases with increasing x. so, what is y for the smallest x ? the smallest x here is 0.

y = 0² + 2 = 2

for x larger or equal to 2, y = (1/2)×x + 5.

it again increases with increasing x. the smallest x here is 2.

y = (1/2)×2 + 5 = 1 + 5 = 6.

so, the smallest possible value for y is 2. and then it will approach positive infinity, when x approaches positive infinity. but it can never reach that (only after infinite time and at infinite x, so it is officially undefined), so that the interval is open on that end.