Question

draw the graph of (f(x) = -\frac{1}{11} cdot (11)^{x+4} - 4)

Explanation:

Step1: Simplify the function

$$f(x) = -11^{-1} \cdot 11^{x+4} - 4 = -11^{x+3} - 4$$

Step2: Identify the asymptote

$$y = -4$$

Step3: Find key points

$$f(-4) = -11^{-1} - 4 = -5$$

$$f(-3) = -11^{0} - 4 = -5$$

$$f(-2) = -11^{1} - 4 = -15$$

Step4: Plot the graph

Draw a curve approaching \(y = -4\) as \(x \to -\infty\) and passing through \((-4, -5)\) and \((-2, -15)\).

Answer:

The graph of \(f(x) = -\frac{1}{11} \cdot (11)^{x+4} - 4\) is an exponential curve with a horizontal asymptote at \(y = -4\), passing through the points \((-4, -5)\) and \((-3, -15)\).