by performing transformations on the parent function f (x) = |x|. The function f(x) = |x| is an absolute value function. The highest or lowest point on the graph of an absolute value function is called the vertex.

So **parent function of absolute value** is y = | x |. If x is positive, it comes out positive (with x ≥ 0, y = x) and if x is negative, it comes out positive (with x < 0, y = -x) so you create a piecewise **function**.

Furthermore, how do you manipulate absolute value? **SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)**

- Step 1: Isolate the absolute value expression.
- Step2: Set the quantity inside the absolute value notation equal to + and – the quantity on the other side of the equation.
- Step 3: Solve for the unknown in both equations.
- Step 4: Check your answer analytically or graphically.

what is the purpose of absolute value?

When you see an **absolute value** in a problem or equation, it means that whatever is inside the **absolute value** is always positive. **Absolute values** are often used in problems involving distance and are sometimes used with inequalities. That’s the important thing to keep in mind it’s just like distance away from zero.

What is a parent function in math?

In **mathematics**, a **parent function** is the simplest **function** of a family of **functions** that preserves the definition (or shape) of the entire family. For example, for the family of quadratic **functions** having the general form. the simplest **function** is.

### What is a piecewise function in math?

In mathematics, a piecewise-defined function (also called a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each sub-function applying to a certain interval of the main function’s domain, a sub-domain.

### What is the difference between an exponential function and a linear function?

Linear functions are straight lines while exponential functions are curved lines. If the same number is being added to y, then the function has a constant change and is linear. If the y value is increasing or decreasing by a certain percent, then the function is exponential.

### Is an absolute value function linear?

Absolute Value Function Family If x = 0, then y = |0| = 0. If x is positive, then the function value is equal to x. Every absolute value graph will take this shape, as long as the expression inside the absolute value is linear.

### How do you tell if an absolute value function opens up or down?

Range: When finding the range of an absolute value function, find the vertex (the turning point). If the graph opens upwards, the range will be greater than or equal to the y-coordinates of the vertex. If the graph opens downward, the range will be less than or equal to the y-coordinate of the vertex.

### How do you graph absolute value functions without a calculator?

Example 1: Solve: Enter left side in Y1. You can find abs( ) quickly under the CATALOG (above 0) ( or MATH → NUM, #1 abs( ) Enter right side in Y2. Use the Intersect Option (2nd CALC #5) to find where the graphs intersect. Move the spider near the point of intersection, press ENTER. Answer: x = 4; x = -4.