Question

Which functions have a range of ..

Answer 1

Options (3) and (5)

Explanation:

Option (1)

f(x) = x² + 7x - 2

= x² + 2(3.5)x + (3.5)² - (3.5)² - 2

= (x + 3.5)² - 14.25

Therefore, vertex of the graph → (-3.5, -14.25)

And the graph will open upwards.

Range of the function → [-14.25, ∞)

Option (2)

f(x) = -(x + 1)² - 4

Since, leading coefficient is negative, curve of the function will open downwards.

Vertex → (-1, -4)

Range of the function → [-4, -∞)

Option (3)

f(x) = -4x + 11

This function is defined for all real values of x.

Range of the function → (-∞, ∞)

Option (4)

f(x) =
`2^(x+3)`

Range of this exponential function → (0, ∞)

Option (5)

f(x) =
`(2)/(3)x-8`

Function is defined for all real values of x.

Range of the function will be (-∞, ∞)

Therefore, Options (3) and (5) are the correct options.