The question asks you to graph the exponential function $g(x) = 3^x$ by plotting five points on the graph.

Here’s how you can calculate five points for $g(x) = 3^x$:

Steps:

1. Choose some values of $x$, such as $x = -2, -1, 0, 1, 2$.
2. Compute $g(x) = 3^x$ for each $x$.

Calculations:

• When $x = -2$: $g(-2) = 3^{-2} = \frac{1}{3^2} = \frac{1}{9} \approx 0.11$
• When $x = -1$: $g(-1) = 3^{-1} = \frac{1}{3} \approx 0.33$
• When $x = 0$: $g(0) = 3^0 = 1$
• When $x = 1$: $g(1) = 3^1 = 3$
• When $x = 2$: $g(2) = 3^2 = 9$

Table of Points:

Plotting:

• On the graph, mark the points:
  • (-2, 0.11)
  • (-1, 0.33)
  • (0, 1)
  • (1, 3)
  • (2, 9)
• Draw a smooth curve through these points, showing the rapid growth of the exponential function.

Let me know if you'd like more details or assistance!

Related Questions:

1. What happens to the graph of $3^x$ if the base is changed to $2$?
2. How does $g(x) = 3^x$ behave as $x \to \infty$?
3. What is the reflection of $g(x) = 3^x$ about the $y$-axis?
4. How do exponential functions differ from linear functions?
5. Can you identify the asymptote of $g(x) = 3^x$?

Tip:

For exponential functions, the base determines how rapidly the function grows or decays. A larger base results in faster growth.