Answer to Question #159131 in Algebra for Jan

Question

using visuals/diagrams, compare and contrast linear and exponential functions. In your discussion, consider using the following talking points: first differences, linear, exponential, equation, graph, f(x)=x, f(x)=2^x. 

Answer 1

Exponential and linear refer to the type of a function by looking at the power of the independent variable. A linear function is one where the independent variable is to the power of 1.

For example, in the linear equation y = mx + b , x is the aforementioned independent variable. The term linear comes from the plot of the function; regardless of the values of m and b

, the graphed function will always be a line.

An exponential function is one where the independent variable is to a non-trivial (not 0 th or 1st) power. These are typical of the form y=a⋅bx

. The term exponential comes from the use of exponentiation in the independent variable.