Question

draw the graph of \\(f(x) = \frac{1}{3} \cdot (3)^{x+3} + 4\\)

Explanation:

Step1: Simplify the function

$$f(x) = 3^{-1} \cdot 3^{x+3} + 4 = 3^{x+2} + 4$$

Step2: Identify the asymptote

$$y = 4$$

Step3: Calculate key points

$$f(-3) = 3^{-1} + 4 = 4.33$$

$$f(-2) = 3^{0} + 4 = 5$$

$$f(-1) = 3^{1} + 4 = 7$$

$$f(0) = 3^{2} + 4 = 13$$

Answer:

The graph of \(f(x) = \frac{1}{3} \cdot (3)^{x+3} + 4\) is an exponential growth curve with a horizontal asymptote at \(y = 4\). Key points to plot on the grid are:

• \((-3, 5)\)
• \((-2, 7)\)
• \((-1, 13)\)