Question

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

Explanation:

Step1: Identify the horizontal asymptote

$$y = 3$$

Step2: Simplify the function expression

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

Step3: Calculate key point at x=3

$$f(3) = -4^{-1} + 3 = 2.75$$

Step4: Calculate key point at x=4

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

Step5: Calculate key point at x=5

$$f(5) = -4^{1} + 3 = -1$$

Answer:

The graph of \(f(x) = -\frac{1}{4} \cdot (4)^{x-3} + 3\) is an exponential curve with a horizontal asymptote at \(y = 3\). It passes through the points \((3, 2.75)\), \((4, 2)\), and \((5, -1)\), decreasing rapidly as \(x\) increases.