Although we are not aware of it, we use functions in many parts of our lives unintentionally. Functions can be used in real-life situations when an inputted value has a specific output value. For example, the distance a car has traveled (the output) is dependent on how long that car has been driving (the input). For another example, a soda, snack, or stamp machine the user puts in money, punches a specific button, and a specific item drops into the output slot. Polynomials are algebraic expressions that consist of variables and coefficients. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses. Trigonometry simply means calculations with triangles. It is a study of relationships in mathematics involving lengths, heights and angles of different triangles. Trigonometry developed from a need to compute angles and distances in such fields as astronomy, mapmaking, surveying, and artillery range finding. Trigonometry may not have its direct applications in solving practical issues, but it is used in various things that we enjoy so much. For example music, as you know sound travels in waves and this pattern though not as regular as a sine or cosine function, is still useful in developing computer music. Exponential functions can grow or decay very quickly. Exponential functions are often used to model things in the real world, such as populations, radioactive materials, and compound interest. In economics exponential functions are important when looking at growth or decay. Example is the value of an investment that increases by a constant percentage each period. Much of the power of logarithms is their usefulness in solving exponential equations. For example,
logarithms are used for measuring the magnitude of earthquakes, used for measuring the noise levels in dBs, used to measure the pH level of chemicals.