How to Graph Absolute Values

A simple absolute value graph should look like a symmetrical “V” because of the absolute value property (the absolute value property makes the left side of the graph look like the right side of the graph--the sides are mirroring each other). An absolute value changes any value of a number to a positive one. Because of its similarity to graphing linear equations, graphing absolute-value functions can be quite tricky. However, correctly graphing this kind of function requires only a few steps.


  1. Image titled Graph Absolute Values Step 1
    Make a T-chart of the function equation. The T-chart is basically two columns—one representing x-values and the other the resulting y-values.
  2. Image titled Graph Absolute Values Step 2
    Pick a number of x-values. You can choose any x-value numbers but be sure to pick numbers from a wide range (e.g. 1,4,7 not 1,2,3) to prevent the graph from being too similar to a linear equation. Write these values in the first column of the T-chart.
  3. Image titled Graph Absolute Values Step 3
    Determine the corresponding y-value from each x-value you chose. To get the y-value of each x-value, substitute the x-value for the x in the given equation, then simplify. The resulting number is the y-value for the given x-value.
    • In the equation, replace every x with your selected x-value (in y=2x, just replace x with your selected x-value [for example, using the number 3] then your equation will be “y=2(3)”) then you simplify it until you get a single number.
    • The result will be your y (in the example y=6 [2 multiplied 3 is 6]).
  4. Image titled Graph Absolute Values Step 4
    Write each y-value in the second column of your T-chart. Place it to the right of its corresponding x-value. For example:
    • If y=|x|+ 1 and you pick the x-values of 4, 1, 0 and -3 then, by substituting these x-values to the equation, the y-values would be 5, 2, 1 and 4 respectively.
    • By substituting an x-value of 4 (for example) into the equation you should get y =|4|+ 1, then by simplifying it will be come y = 4 + 1 then y = 5.
    • Proceed to do the same with your other x-values to get their corresponding y-values.
  5. Image titled Graph Absolute Values Step 5
    Make a Cartesian plane in a graphing paper. To make it, draw two lines-- one vertical and the other horizontal (they should be perpendicular to each other). The vertical line is called y-axis, the horizontal line is the x-axis, and the point where the lines intersect is called the origin
  6. Image titled Graph Absolute Values Step 6
    Plot the points. An x-value and its corresponding y-value determines a point.
    • The x-value will tell you how far you need to go towards the right of the x-axis (or left if the x-value is negative).
    • The y-value will tell you how far you need to go up along the y-axis (or down if the y-value is negative).
  7. Image titled Graph Absolute Values Step 7
    Connect the points. Connect them from x-value to x-value.
    • If you graphed a straight line, you might need to plot more points of a wider range as you may have only plotted one side of the equation, or just one side of your “V”.
    • If you plotted a diagonal line sloping down towards the right (or a line looking like a backslash on your keyboard “\”), you might want to plot points of greater x-value (or of lesser x-value if your diagonal looks like the opposite slash) until the other side of your V shows up.
  8. Image titled Graph Absolute Values Step 8
    Look for a symmetrical V shape. You can determine if you got the graph right if, from the line of symmetry, the left side is symmetrical to the right (if they look the same).
    • The final graph should look like a V because instead of the left side of the graph continuing the slope of the right side, it will actually “bend”.
    • Thus both sides of the graph will mirror each other, similar to the letter V.


  • During graphing, a common mistake a lot of people make is to just get the points from consecutive x-values (or points near each other). Doing this might make just a line or a single side of your V, as this will just plot the points only from that side.
  • In order to prevent this, try plotting more points towards one side (to where you think it should bend to) and thus graphing the other side of your V.

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Categories: Mathematics | Algebra