Answer:
The function given by [tex]y = - (2)^{x} + 3[/tex] will have a range of y < 3.
Step-by-step explanation:
The function given by [tex]y = - (2)^{x} + 3[/tex] will have a range of y < 3.
This is because, for any real values of x, the term [tex]- (2)^{x}[/tex] will have a negative value. If we put x = 1, then, [tex]- (2)^{x}[/tex] = - 2, and for x = -1, then [tex]- (2)^{x}[/tex] = - 0.5.
That means [tex]- (2)^{x} < 0[/tex] for all real x.
Hence, [tex]- (2)^{x} + 3[/tex] < 0 + 3
⇒ y < 3 for all real x. (Answer)
