Station 1: 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 of the form y = ab^x, where a is a constant, b is the base (a positive number), and x is the exponent. The graph of an exponential function increases or decreases rapidly.

Front

What does the slope of a linear function represent?

Back

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

Front

What is the y-intercept in a linear equation?

Back

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

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 x-values and y-values. If the differences in y-values divided by the differences in x-values are constant, the function is linear.

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 over equal intervals, while exponential growth increases by a constant percentage over equal intervals.

Front

What does it mean if a function is neither linear nor exponential?

Back

If a function is neither linear nor exponential, it does not fit the characteristics of either type, often showing a more complex relationship between variables.

Front

How can you graph a linear function?

Back

To graph a linear function, you can plot the y-intercept on the y-axis and use the slope to find another point. Draw a straight line through these points.

Front

What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3.