Absolute Value Equation Calculator
Introduction & Importance
Absolute value equations are crucial in mathematics, physics, and engineering. They help model real-world situations where only the magnitude, not the direction, matters.
How to Use This Calculator
- Enter your equation using |x| for absolute value.
- Enter the value of x.
- Click ‘Calculate’.
Formula & Methodology
The formula for an absolute value equation is y = |f(x)|, where f(x) is your function. The calculator solves for y and graphs the result.
Real-World Examples
Example 1: Distance
If a particle moves according to the equation s = |3t – 2|, where s is the distance from the origin and t is time in seconds, how far is the particle from the origin after 3 seconds?
Solution: s = |3(3) – 2| = 7
Example 2: Speed
If a car’s speed is given by v = |10 – t|, where v is speed in mph and t is time in hours, what is the car’s speed after 5 hours?
Solution: v = |10 – 5| = 5 mph
Data & Statistics
| Function | Absolute Value | Regular |
|---|---|---|
| f(x) = x | y = |x| | y = x |
| f(x) = x^2 | y = |x^2| | y = x^2 |
| Property | Value |
|---|---|
| Domain | All real numbers |
| Range | [0, ∞) |
Expert Tips
- Use absolute value functions to model real-world situations where only the magnitude matters.
- Be careful with the domain and range of absolute value functions.
- Graphing absolute value functions can be tricky. Use this calculator to help!
Interactive FAQ
What is the domain of y = |f(x)|?
The domain is all real numbers.
What is the range of y = |f(x)|?
The range is [0, ∞).
How do I graph y = |f(x)|?
Reflect the part of the graph of y = f(x) that is below the x-axis over the x-axis, and then shift the graph up or down if necessary.