Question

(use a comma to separate answers as needed c. {y|y > 0} d. {y|y < } e. all real numbers the y-intercept of the function f(x)=7·3^x is 7. (type an integer or a decimal.) the asymptote of f(x)=7·3^x is. (type an equation.))

Explanation:

Step1: Recall exponential function properties

For $f(x)=a \cdot b^x$ where $a>0, b>1$, as $x \to -\infty$, $b^x \to 0$.

Step2: Find the limit

$$\lim_{x \to -\infty} 7 \cdot 3^x = 7 \cdot 0 = 0$$

Step3: Identify the asymptote

The function approaches $y=0$ and never crosses it, so this is the horizontal asymptote.

Answer:

$y=0$