Home >> Science & Nature >> Science

How to Graph an Absolute Value Function With Two Variables & a Negative Coefficient

A function is a mathematical relationship where an "x" value produces one, and only one, "y" value. An absolute value function includes a term, or terms, within an absolute value symbol, which is represented with vertical bars, such as | x |. The operation of the bars is to make the answer of the inside terms a positive value. For example, |-3| = 3. But if there is a term that needs to be solved within the bars, such as |4x + 3|, the x-value needs to be solved for both the positive and negative possibilities as the sign of "x" would change the solution within the brackets and thus the final answer.

Instructions

- 1
  Graph the absolute value function of y = |-4x + 2| by finding points using a t-chart, a two column chart with the left column labeled "x" and the right labeled y = |-4x + 2|. Select six points for the t-chart, three negative and three positive. Use -3, -2, -1 and 1, 2 and 3.
- 2
  Plug each x-value into the function to solve for its y-value. Start with -3: |-4 * -3 + 2| = |14| = 14 or point (-3, 14). Solve for -2: |-4 * -2 + 2| = 10 or point (-2, 10). Solve for -1: |-4 * -1 + 2| = 6 or point (-1, 6). Solve for 1: |-4 * 1 + 2| = |-2| = 2 or point (1, 2). Solve for 2: |-4 * 2 + 2| = |-6| = 6 or point (2, 6). Solve for 3: |-4 * 3 + 2| = |-10| = 10 or point (3, 10).
- 3
  Graph the found points on a coordinate graph. Draw a line to connect the dots, placing arrows on each end of the line to represent continuation.

Science