How can you test the equivalence of two expressions using tables and graphs?

Answer 1

You can test for inequality but not for equality.

You can take different values of the independent variable or argument of the expression (usually denoted by x), and calculate the dependent variable or the value of the expression (usually denoted by y). These can be tabulated or shown on a graph. If the y-values for the same x-values are different, then the two expressions are different. But even if they all match perfectly, you cannot say that they are equivalent because there could be other x-values - which you did not test - for which the y-values are different.

For example, consider

f(x) = x^2 + 4

and

g(x) = x^3 - 3x^2 - 5x + 4

then f(-1) = 5 = g(-1)

f(0) = 4 = g(0)

and f(5) = 29 = g(5)

but for any other integer value of x, the values of the two expressions are different. However, your test did not pick that up.

You could increase the number of points tested but there will be other expressions such that the two can match at any number of selected points and still be different elsewhere.