Question

draw the graph of (f(x) = \frac{1}{7} cdot (7)^{x-4} + 3)

Explanation:

Step1: Simplify the function

$$f(x) = 7^{-1} \cdot 7^{x-4} + 3 = 7^{x-5} + 3$$

Step2: Identify the asymptote

$$y = 3$$

Step3: Calculate key points

$$f(4) = 7^{-1} + 3 \approx 3.14$$

$$f(5) = 7^{0} + 3 = 4$$

$$f(6) = 7^{1} + 3 = 10$$

Step4: Plot and connect

Plot the points \((4, 3.14)\), \((5, 4)\), \((6, 10)\) and sketch the curve.

Answer:

To draw the graph of \(f(x) = \frac{1}{7} \cdot (7)^{x-4} + 3\), plot the horizontal asymptote at \(y = 3\) and the key points \((4, 3.14)\), \((5, 4)\), and \((6, 10)\), then draw a smooth curve rising from left to right.