Linear and Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term of a geometric sequence is multiplied to get the next term. It is found by dividing any term by the previous term.

Front

How do you identify exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in a rapid increase. The graph of an exponential growth function rises steeply.

Front

How do you identify exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over time, leading to a rapid decrease. The graph of an exponential decay function falls steeply.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis. It is the value of f(x) when x = 0.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while exponential functions have a variable rate of change and graph as curves.