1. **Understanding Exponential Functions:** An exponential function has the form $$y = a \cdot b^x$$ where $a \neq 0$, $b > 0$, and $b \neq 1$. The base $b$ determines the growth or decay. 2. **Finding the y-intercept:** The y-intercept occurs when $x=0$. Substitute $x=0$ into the function: $$y = a \cdot b^0 = a \cdot 1 = a$$ So, the y-intercept is at $(0, a)$. 3. **Finding the x-intercept:** The x-intercept occurs when $y=0$. Set the function equal to zero: $$0 = a \cdot b^x$$ Since $a \neq 0$ and $b^x > 0$ for all real $x$, the function never equals zero. Therefore, there is **no x-intercept**. 4. **Finding the asymptote:** Exponential functions have a horizontal asymptote. For $$y = a \cdot b^x + c$$ the asymptote is $y = c$. If $c=0$, the asymptote is the x-axis: $$y=0$$. 5. **Plotting the function:** - Plot the y-intercept at $(0, a)$. - Choose several $x$ values (e.g., $-2, -1, 1, 2$) and calculate corresponding $y$ values. - Draw a smooth curve through these points approaching the asymptote. Example: For $$y = 2 \cdot 3^x$$ - y-intercept: $(0, 2)$ - Asymptote: $y=0$ - Points: $x=-1 \Rightarrow y=2 \cdot 3^{-1} = \frac{2}{3}$, $x=1 \Rightarrow y=6$ This shows exponential growth. **Summary:** - y-intercept at $(0, a)$ - No x-intercept - Horizontal asymptote at $y=c$ - Plot points and draw curve approaching asymptote