Question

Graph: f(x) = 4^x

Answer 1

Do you want a plotted image, or a description + code to plot it yourself? Below is a concise description of the graph and a short Python example you can run to draw it.

Key properties
- Function: f(x) = 4^x
- Domain: (-∞, ∞)
- Range: (0, ∞)
- y-intercept: f(0) = 1
- No x-intercepts (never zero)
- Horizontal asymptote: y = 0 as x → -∞
- Monotonic: strictly increasing for all x
- Concavity: convex (second derivative > 0)
- Derivative: f'(x) = ln(4) · 4^x
- Inverse: f^(-1)(y) = log_4(y) = ln(y)/ln(4)

Some sample points
- f(-2) = 1/16 = 0.0625
- f(-1) = 1/4 = 0.25
- f(0) = 1
- f(1) = 4
- f(2) = 16

Quick ASCII sketch (very rough)
y
^
| *
| *
| *
| *
| *
| *
| *
| *
+-----------------------------> x
-2 -1 0 1 2

Python (Matplotlib) to plot
```python
import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(-4, 3, 400)
y = 4**x

plt.figure(figsize=(6,4))
plt.plot(x, y, label='f(x)=4^x')
plt.axhline(0, color='gray', linewidth=0.7)
plt.scatter([ -2,-1,0,1,2 ], [4**-2,4**-1,1,4,16], color='red')
plt.ylim(-0.1, 18)
plt.xlim(-4, 3)
plt.xlabel('x')
plt.ylabel('f(x)')
plt.title('Graph of f(x)=4^x')
plt.grid(True, which='both', ls=':', lw=0.5)
plt.legend()
plt.show()
```

If you want, I can generate and send the actual image (PNG/SVG), or produce a high-resolution plot or interactive plot. Which would you prefer?