Question

Q5 Graph the exponential function y=5(2)^x

Answer 1

To graph y = 5·2^x:

Key features
- Domain: (-∞, ∞)
- Range: (0, ∞)
- Horizontal asymptote: y = 0
- y-intercept: (0, 5)
- No x-intercept (never crosses x-axis)
- Increasing exponential (base 2 > 1): as x increases, y doubles for each +1 in x.

Helpful points to plot
- x = -2 → y = 5·2^-2 = 1.25 → (-2, 1.25)
- x = -1 → y = 2.5 → (-1, 2.5)
- x = 0 → y = 5 → (0, 5)
- x = 1 → y = 10 → (1, 10)
- x = 2 → y = 20 → (2, 20)
- x = 3 → y = 40 → (3, 40)

How to sketch
1. Draw the horizontal asymptote y = 0.
2. Plot the points from the table (especially (0,5) and (1,10)).
3. Connect them with a smooth curve that approaches y = 0 as x → -∞ and rises steeply to the right.

Optional: solve for a given y. Example: when y = 1, 5·2^x = 1 ⇒ 2^x = 0.2 ⇒ x = log2(0.2) ≈ -2.322.