3. For the function $$ f(x)=-4 \cdot(0.3)^{x}+1 $$, identify the $$ y $$-intercept and asymptote. $$ y $$-intercept: Asymptote:

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To identify the $$ y $$-intercept and the asymptote of the function $$ f(x) = -4 \cdot (0.3)^{x} + 1 $$, let's analyze each component step by step.

### 1. $$ y $$-Intercept

The $$ y $$-intercept of a function is the point where the graph crosses the $$ y $$-axis. This occurs when $$ x = 0 $$.

**Calculation:**
$$
f(0) = -4 \cdot (0.3)^{0} + 1
$$
$$
f(0) = -4 \cdot 1 + 1
$$
$$
f(0) = -4 + 1 = -3
$$

**$$ y $$-Intercept:**
$$
(0, -3)
$$

### 2. Asymptote

An asymptote is a line that the graph of a function approaches but never touches. For exponential functions of the form $$ f(x) = A \cdot b^{x} + C $$, the horizontal asymptote is given by $$ y = C $$.

In the given function:
$$
f(x) = -4 \cdot (0.3)^{x} + 1
$$
Here, $$ C = 1 $$.

**Asymptote:**
$$
y = 1
$$

### **Summary**

- **$$ y $$-Intercept:** $$ (0, -3) $$
- **Asymptote:** $$ y = 1 $$
$$ y $$-intercept: $$ (0, -3) $$ Asymptote: $$ y = 1 $$

3. For the function \( f(x)=-4 \cdot(0.3)^{x}+1 \), identify the \( y \)-intercept and asymptote. \( y \)-intercept: Asymptote:

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