Answer:
Options (3) and (5)
Step-by-step 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) = [tex]2^{x+3}[/tex]
Range of this exponential function → (0, ∞)
Option (5)
f(x) = [tex]\frac{2}{3}x-8[/tex]
Function is defined for all real values of x.
Range of the function will be (-∞, ∞)
Therefore, Options (3) and (5) are the correct options.
