Question

Describe the end behavior, and intervals of increase/decrease for the exponential function graphed below.
(0,1) (-1,4)


(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
End Behavior:
As x approaches −∞
, f(x)
approaches Response area
As x approaches ∞
, f(x)
approaches Response area



Intervals of Increase/Decrease:

The exponential function is Response area from Response area to Response area.

t

Answer 1

To analyze the given points and the behavior of the exponential function that passes through them, we can derive information about its end behavior and intervals of increase/decrease.

1. **End Behavior**:
- As an exponential function typically approaches 0 (the horizontal asymptote) as \( x \) approaches negative infinity \( (-\infty) \):
- As \( x \) approaches −∞, \( f(x) \) approaches 0 (the horizontal asymptote).
- As \( x \) tends toward positive infinity \( (+\infty) \):
- As \( x \) approaches ∞, \( f(x) \) approaches infinity (\( +∞ \)).

2. **Intervals of Increase/Decrease**:
- Exponential functions are always increasing. Therefore:
- The exponential function is increasing from \( -∞ \) to \( +∞ \).

Here’s how to fill in the responses:

**End Behavior:**
- As x approaches −∞, f(x) approaches **0**.
- As x approaches ∞, f(x) approaches **+∞**.

**Intervals of Increase/Decrease:**
- The exponential function is **increasing** from **−∞** to **+∞**.

Therefore, the complete inputs would be:

**End Behavior:**
- As x approaches −∞, f(x) approaches **0**.
- As x approaches ∞, f(x) approaches **+∞**.

**Intervals of Increase/Decrease:**
- The exponential function is **increasing** from **−∞** to **+∞**.