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 does the slope of a linear function represent?

Back

The slope represents the rate of change of the function; it indicates how much the y-value changes for a one-unit increase in the x-value.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented as (0, b) in the function f(x) = mx + b.

Front

How do you identify exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over equal time intervals, resulting in a J-shaped curve on a graph.

Front

How do you identify exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over equal time intervals, resulting in a curve that approaches zero but never touches it.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease at a constant rate, while exponential functions increase or decrease at a rate proportional to their current value.

Front

How do you find the x-intercept of a linear function?

Back

To find the x-intercept, set f(x) = 0 and solve for x.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, the value of f(x) also increases.