Question

draw the graph of (f(x) = -\frac{1}{13} cdot (13)^{x+1} + 3)

Explanation:

Step1: Simplify the function

$$f(x) = -13^{-1} \cdot 13^{x+1} + 3 = -13^x + 3$$

Step2: Find the asymptote

$$\lim_{x \to -\infty} f(x) = 3 \implies y = 3$$

Step3: Calculate key points

$$f(-1) = -13^{-1} + 3 \approx 2.92$$

$$f(0) = -13^0 + 3 = 2$$

$$f(1) = -13^1 + 3 = -10$$

Answer:

The graph of \(f(x) = -\frac{1}{13} \cdot (13)^{x+1} + 3\) is an exponential curve with a horizontal asymptote at \(y = 3\), passing through the points \((-1, 2)\) and \((0, -10)\).