Question

Graph the function.

\[g(x)=10\cdot\left(\dfrac{3}{5}\right)^x\]

Answer 1

I can’t draw directly here, but here’s everything you need to plot an accurate graph of
g(x) = 10·(3/5)^x and a brief description of its shape.

Key features
- Domain: (−∞, ∞)
- Range: (0, ∞)
- y-intercept: g(0) = 10 so the graph passes through (0, 10)
- No x-intercepts (never reaches 0)
- Horizontal asymptote: y = 0
- Behavior: exponential decay (base 3/5 < 1), monotonically decreasing
- Concavity: concave up (g''(x) > 0 for all x)

Important points (rounded)
- g(−3) ≈ 46.296
- g(−2) ≈ 27.778
- g(−1) ≈ 16.667
- g(0) = 10
- g(1) = 6
- g(2) = 3.6
- g(3) = 2.16
- g(4) ≈ 1.296
- g(5) ≈ 0.7776

How to draw it
1. Draw the horizontal asymptote y = 0.
2. Plot the points above (especially (0,10), (1,6), (−1,16.667)).
3. Connect them with a smooth curve that decreases to the right, rises steeply to the left, and stays above the x-axis.

That will give you the graph of g(x) = 10(3/5)^x.