Comparing Functions

There are many ways to represent functions. For example, a function can be represented with an input-output table, with a graph, and with an equation.

Sometimes a problem asks us to compare two functions which are represented in different ways. For example, you might be given a table and a graph, and asked which function is greater for a particular value, or which function increases faster.

Example :

Two functions are represented in different ways.

Function 1: The input-output table shows the x - and y -values of a quadratic function.

Function 2: The graph of a linear function is shown.

From the two functions, which function grows faster for large positive values of x?

In the graph, the y-intercept is 5 and the slope is 1. So, for x = 0, the function shown in the graph has a greater value. Also, since the slope is positive, it's increasing.

However, if you look at the values in the table, you will see that the y -values are equal to the square of x . These values will have a faster-than-linear rate of growth.

For example, for the function in the table, when x = 8, y = 64. You can see in the graph that the line is not yet that high when x = 8.