Rearrange the algebra equation so that the dependent variable y is expressed in terms of x. That is, the variable y is on the right side of the equal (=) sign and the x variables are on the left side of the equal sign.
Examine the rearranged algebra equation. Observe whether or not the equation has a square root term in it. Algebra equations that contain a square root, such as y = Square Root (x) will have two values of y for each value of x. For this equation, if a value of 4 is used for x, you will obtain two values of x, -2 and 2, since the square of 4 is 2 and -2. Therefore, y = Square Root (x) is not a function.
Examine the rearranged algebra equation again. Observe whether or not the equation has an even root term higher than 2, such as the root of 4, 6 or 8. Algebra equations that contain an even root, such as y = Fourth Root (x) will have two values of y for each value of x. For this equation, if a value of 16 is used, you will obtain two values of x, -2 and 2, since the fourth root of 16 is 2 or -2. Therefore, y = Fourth Root (x) is not a function.
Plot the equation on graph paper using the vertical axis as the dependent y coordinate and the horizontal axis as the independent x coordinate. Determine whether or not you can draw an imaginary vertical line through the plot such that it will intersect the plot of the equation at two or more points. If it does, the equation is not a function. If you can't find a vertical line that will intersect the graph of the equation at two or more points, the equation is a function.