Help With Function Tables in Math

Students learning basic algebra often struggle with mathematical function tables. Function tables allow you to solve basic algebra equations by finding the value of the unknown variable. Organizing information in a function table is a visualization strategy that helps students understand algebraic equations. You must know basic addition, subtraction, multiplication and division to solve basic function tables.

Concepts

Solving function tables tests your knowledge of basic algebraic rules. Some function tables require you to solve an equation after specifying a value for the unknown variable. Others provide a set of coordinates and ask you to determine the equation governing the values. Becoming familiar with function tables helps you understand how algebraic equations work and how to solve them.

Table Form

A standard function table is T-shaped with an algebraic equation in the form y = ax + b across the top. Values for x form a column on the left, while y values go on the right. Although a completed function table contains an equation and a full series of values, fields are often left blank for students to solve. Filling in an incomplete function allows you to understand how equations work.

Solving for Y

Some function tables have a completed algebraic function with an incomplete y-value column. Plugging each x value into the equation yields the corresponding y value in the same row. Consider a function table with the equation y = 3x + 2 and the number 3 in the x-value column. Solve for y by plugging x = 3 into the equation: y = 3*3 + 2 = 11, with the "*" symbol denoting multiplication. Write 11 in the x = 3 row of the y column. Solve for each additional y value in the same way.

Solving for X

If a function table has an incomplete x-value column, use the provided y-values to solve for x. Consider the same equation y = 3x + 2 and the number 14 in the y-value column. Plug 14 into the equation for the variable y: 14 = 3x + 2. Subtract 2 from each side, yielding 12 = 3x. Divide each side by 3 to solve for x: 12/3 = x = 4. Thus, when x equals 4, y equals 14. Solve the remaining spaces in the table by plugging y values into the equation and solving for x.

Solving for the Equation

Some function tables contain a complete set of x and y values but no equation. Use the provided values to determine the equation governing the table. Think of the table values of a set of (x,y) coordinates. For example, the coordinates (1,13) correspond to an x value of 1 and a y value of 13. Consider the following set of (x,y) coordinates: (1,13), (3,15), (6,18) and (9,21). Look for patterns between the x and y values. In this case, there is a difference of 12 between each set of values. Thus, the equation is y = x + 12. Plug in a provided x value to double-check your work. When x = 3, y = 3 + 12 = 15, illustrating that the equation is correct.