To graph the function $ y = |2x| $, here are the steps:

1. **Understand the Absolute Value Function**:
   - The absolute value $ |2x| $ means that the output is always non-negative.
   - $ y = 2x $ for $ x \geq 0 $.
   - $ y = -2x $ for $ x < 0 $.

2. **Plot Key Points**:
   - When $ x = 0, y = 0 $.
   - For positive $ x $, calculate $ y $ using $ 2x $. Example: $ x = 1, y = 2; x = 2, y = 4 $.
   - For negative $ x $, calculate $ y $ using $ -2x $. Example: $ x = -1, y = 2; x = -2, y = 4 $.

3. **Shape**:
   - The graph will have a "V" shape, symmetric about the $ y $-axis, opening upwards.

I’ll graph it for you. One moment. numpy as np
import matplotlib.pyplot as plt

# Define the function y = |2x|
x = np.linspace(-5, 5, 500)
y = np.abs(2 * x)

# Plot the graph
plt.figure(figsize=(8, 6))
plt.plot(x, y, label=r"$y = |2x|$", color='blue')
plt.axhline(0, color='black',linewidth=0.5, linestyle='--')  # x-axis
plt.axvline(0, color='black',linewidth=0.5, linestyle='--')  # y-axis

# Add labels and title
plt.title("Graph of $y = |2x|$", fontsize=14)
plt.xlabel("$x$", fontsize=12)
plt.ylabel("$y$", fontsize=12)
plt.grid(color='gray', linestyle='--', linewidth=0.5)
plt.legend(fontsize=12)
plt.show()Here is the graph of $ y = |2x| $. The "V" shape reflects the absolute value, symmetric about the $ y $-axis.

Would you like a detailed explanation of the graph or help with a related question?  

Here are 5 related questions for exploration:
1. How does changing the coefficient (e.g., $ y = |kx| $) affect the graph?
2. What happens to the graph if we add a constant (e.g., $ y = |2x| + 3 $)?
3. How does the graph of $ y = |x| $ compare to $ y = |2x| $?
4. What is the domain and range of $ y = |2x| $?
5. How do we write the piecewise form of $ y = |2x| $?

**Tip**: When graphing absolute value functions, always start by finding the vertex and analyzing symmetry.

Learn how to graph the function y = |2x| with a step-by-step solution. This problem explains absolute value functions, piecewise definitions, and graphing techniques. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation