Comparing Functions

Question

The function f(x) is shown on the graph.

Which type of function describes f(x)?

 Rational 

Polynomial 

Logarithmic 

Exponential

Answer 1

Hey!

Four easy tips to help you remember which is which (just using the graph).

Rational - typically these have at least one asymptote. This is a value that the graph is avoiding - it approaches it but never reaches it. Since these are written as ratios, it is the value(s) that make the denominator zero.

Polynomial - Many different types but these don't have asymptotes. They are always smooth continuous curves that extend infinitely across the real number line (unless bounded by an interval).

Logarithmic/Exponential Graphs. - These are inverse functions! The logarithmic graphs will "shoot off" to infinity on the x-axis (asymptotic on the y-axis), while the exponential will "shoot off" to infinity on the y-axis (asymptotic on the x-axis)! - Memorize at least one of these and how it looks!

Hope this narrows it down!