Answer:
Option (4) and (5)
Step-by-step explanation:
Option (1)
f(x) = -(x + 1)² - 4
Since, given function has the vertex = (-1, -4) and the parabola is the opening downwards,
Range of the function → (-∞, -4]
Option (2)
f(x) = [tex]2^{x+3}[/tex]
Horizontal asymptote of the function is,
y = 0
Therefore, range of the given function → (0, ∞)
Option (3)
f(x) = x² + 7x - 9
= x² + 2(3.5)x + (3.5)² - (3.5)² - 9
= (x + 3.5)²- 12.25 - 9
= (x + 3.5)²- 21.25
Vertex of the parabola is (-3.5, -21.25) and parabola is opening upwards.
Therefore, range of the function → [-21.25, ∞)
Option (4)
f(x) = -4x + 11
Range of this function is (-∞, ∞).
Option (5)
f(x) = [tex]\frac{2}{3}x-8[/tex]
Range of the function is (-∞, ∞).
Options (4) and (5) are the correct options.
