Use the sketch of the exponential function.

Question

The coordinate grid has x and y axes from negative 5 to 5. An exponential function is shown.

Which statement is true about the key features of the exponential function?

(1 point)
Responses

The function has the following end behavior:
as x→−∞,y→0
and
as x→∞,y→−∞
.
The function has the following end behavior: as x rightarrow negative infinity comma y rightarrow 0 and as x rightarrow infinity comma y rightarrow negative infinity .

The function has an x-intercept at 1.5
.
The function has an x -intercept at 1 point 5 .

The function does not have a y-intercept.
The function does not have a y -intercept.

The function is increasing.
The function is increasing.

Answer 1

The correct statement about the key features of the exponential function is:

The function is increasing.

To elaborate on the other statements:

1. The end behavior of exponential functions generally shows that as \( x \to -\infty \), \( y \to 0 \) (approaching the x-axis) and as \( x \to \infty \), \( y \to \infty \). Therefore, the part about \( y \to -\infty \) as \( x \to \infty \) is incorrect.

2. An exponential function of the form \( y = a \cdot b^x \) (where \( b > 1 \)) does not have an x-intercept. It intersects the y-axis but does not cross the x-axis.

3. The correct statement regarding the y-intercept is that the exponential function has one at \( (0, a) \) (where \( a \) is the value when \( x = 0 \)).

Hence, the only correct feature here is that the function is indeed increasing.