Question

Describe the end behavior of the exponential function graphed below.
y intercept 1.5 its on the positive side facing right

As x approaches negative infinity, f(x) approaches ___.

As x approaches infinity, f(x) approaches ___.

infinity
negative infinity
0
1
2

Answer 1

For the exponential function you described, the general form is \( f(x) = a \cdot b^x \), where \( a \) is the y-intercept and \( b \) is a positive constant.

Given that the y-intercept is 1.5, we can infer that the function starts at \( (0, 1.5) \) when \( x = 0 \).

### End Behavior:
1. **As \( x \) approaches negative infinity (\( x \to -\infty \))**:
Exponential functions of the form \( b^x \) (where \( b > 1 \)) decrease towards zero as \( x \) becomes more negative. Thus, as \( x \to -\infty \), \( f(x) \) approaches \( 0 \).

2. **As \( x \) approaches positive infinity (\( x \to \infty \))**:
Exponential functions grow without bound as \( x \) increases. Therefore, as \( x \to \infty \), \( f(x) \) approaches \( \infty \).

### Summary of End Behavior:
- As \( x \to -\infty \), \( f(x) \) approaches **0**.
- As \( x \to \infty \), \( f(x) \) approaches **infinity**.