Often asked: How To Graph Absolute Value Functions?

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


  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?


  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.
  4. Step 4: Check your answer analytically or graphically.

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.

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