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.
Two functions are represented in different ways.
Function : The input-output table shows the - and -values of a quadratic function.
Function : The graph of a linear function is shown.
From the two functions, which function grows faster for large positive values of ?
In the graph, the -intercept is and the slope is . So, for , 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 -values are equal to the square of . These values will have a faster-than-linear rate of growth.
For example, for the function in the table, when , . You can see in the graph that the line is not yet that high when .