# Often asked: How To Graph Absolute Value Functions?

## How do you graph an absolute value function step by step?

GRAPHING ABSOLUTE VALUE FUNCTIONS

1. Step 1: Before graphing any absolute value function, first we have to graph the parent function: y = |x| Its vertex is (0,0)
2. Step 2: Write the given absolute value function as. y – k = |x – h|
3. Step 3: To get the vertex of the absolute value function above, equate (x – h) and (y – k) to zero, That is,

## What is the graph of the absolute value equation?

f (x ) = – | x + 2| + 3 In general, the graph of the absolute value function f (x ) = a| x – h| + k is a “V” with vertex (h, k), slope m = a on the right side of the vertex (x > h) and slope m = – a on the left side of the vertex (x < h).

## How do you graph absolute value parent functions?

The absolute value function is defined by f (x) = |x|. This is the absolute value parent function. The graph of y = a|x| is graph of y = |x| vertically stretched or compressed depending on the |a|. The graph of y = a|x| is graph of y = |x| reflected across the xaxis.

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## How do you graph absolute value on a calculator?

Example 1: Solve:

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

## What is the absolute value of 8?

Absolute value is always nonnegative, since distance is always nonnegative. For example, the absolute value of 8 is 8, since 8 is 8 units from 0 on the number line. The absolute value of − 8 is also 8, since − 8 is also 8 units from 0 on the number line.

## How do you solve an absolute value function?

SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE (S)

1. Step 1: Isolate the absolute value expression.
2. Step2: Set the quantity inside the absolute value notation equal to + and – the quantity on the other side of the equation.
3. Step 3: Solve for the unknown in both equations.

## What is the greatest integer function?

The Greatest Integer Function is also known as the Floor Function. It is written as f(x)=⌊x⌋. The value of ⌊x⌋ is the largest integer that is less than or equal to x.

## What are the key features of the graph of the absolute value function?

We see that the graph of the absolute value function ‘has a V shape, and it satisfies all of the characteristics listed. Its domain is all real numbers; its range is all real numbers greater than or equal to zero; its graph lies completely above the x-axis; and its graph is symmetric with respect to the y-axis.

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## Does every graph represent a function?

The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output. A function has only one output value for each input value. 