Graphs of exponentials and logarithms

The  exercise appears under the Algebra II Math Mission. This exercise works with recognizing graphs of exponential and logarithmic functions.

Types of Problems
There are two types of problems in this exercise:


 * 1) Match the exponential function with it's graph: This problem provides a set of graphs and rules for some exponential functions. The student is asked to match each function with the correct graph.Goeal1.png
 * 2) Match the logarithmic function with it's graph: This problem provides a set of graphs and rules for some logarithmic functions. The student is asked to match each function with the correct graph.Goeal2.png

Strategies
Knowledge of exponent and logarithm graphs, as well as functional transformations are encouraged to ensure success on this exercise.
 * 1) Exponential graphs grow very quickly as x tends to infinity.
 * 2) Logarithmic graphs grow very slowly as x tends to infinity.
 * 3) Adding and subtracting constants perform translations on functions.
 * 4) Multiplying and dividing by constants performs stretch and compression effects.
 * 5) The graphs can be determined and assigned by the asymptotes, which can increase efficiency.

Real-life Applications

 * 1) Logarithms are useful in many scales, such as Richter, Decibel and pH.
 * 2) Exponentials can be used to model things that grow by a relative rate, for example, compound interest and population.