Station 1: Linear Vs. Exponential

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. 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 is in the exponent. It can be expressed in the form y = b(r)^x, where b is a constant, r is the base, and x is the exponent.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified by a straight line on the graph, indicating a constant rate of change.

Front

How can you identify an exponential function from a graph?

Back

An exponential function can be identified by a curve that increases or decreases rapidly, showing a variable rate of change.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

What does the y-intercept of a linear function represent?

Back

The y-intercept of a linear function is the point where the graph crosses the y-axis, indicating the value of y when x is 0.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a percentage of the current value, leading to faster growth over time.

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, indicating that as x increases, y decreases.

Front

Can an exponential function have a negative base?

Back

No, an exponential function cannot have a negative base when dealing with real numbers, as it would lead to complex numbers.