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.