Linear Vs Exponential

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 y = 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 function in which an independent variable appears in the exponent. It can be expressed in the form y = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the values. This means that the difference between consecutive y-values divided by the difference between consecutive x-values will be the same.

Front

How can you identify an exponential function from a table of values?

Back

An exponential function will have a constant ratio between consecutive y-values. This means that each y-value is multiplied by the same factor to get the next y-value.

Front

What does the graph of a linear function look like?

Back

The graph of a linear function is a straight line that can slope upwards, downwards, or be horizontal.

Front

What does the graph of an exponential function look like?

Back

The graph of an exponential function shows rapid growth or decay, forming a curve that increases or decreases sharply.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x, often represented as 'm' in the equation y = mx + b.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by 'b' in the equation y = mx + b.

Front

What is the starting point of an exponential function when a = 1?

Back

The starting point of an exponential function when a = 1 is at (0, 1), meaning when x = 0, y = 1.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much faster growth over time.