Question

The function f(x)=3(2.5)^x is shown on the coordinate plane.

Select from the drop-down menus to correctly describe the end behavior of f(x) .

As x decreases without bound, the graph of f(x)
_______
(approaches y=0
increases without bound
decreases without bound)

As x increases without bound, the graph of f(x)
_______
(approaches y=0
increases without bound
decreases without bound)

Answer 1

The function f(x)=3(2.5)^x is shown on the coordinate plane.

Select from the drop-down menus to correctly describe the end behavior of f(x) .


As x increases without bound, the graph of f(x) increases without bound

Answer 2

As x decreases without bound, the graph of f(x) approaches y = 0.

We can observe in the graph that the exponential functions is approaching to y = 0 as x decreases on the left side of the curve. Also, this behaviour is common on exponential function, because due to the variable is an exponent, the range cannot take negative values.

As x increases without bound, the graph of f(x) increases without bound.

In the graph we can observe that at the right side of the curve, the function is increasing without bound, that is, with no restrictions. In addition, this is a common behaviour of exponential function, the tend to increase without bounds, that's why these functions are used to model problems about population increase, or bacterial reproductions.