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 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 f(x) = a(b)^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

How do you identify a linear equation from a graph?

Back

A linear equation will produce a straight line when graphed, indicating a constant rate of change.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

What is the common ratio in an exponential function?

Back

The common ratio is the factor by which the function's value multiplies for each unit increase in x.

Front

How can you determine if a function is linear or exponential?

Back

If the function's rate of change is constant, it is linear. If the rate of change increases or decreases multiplicatively, it is exponential.

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 constant percentage.

Front

How do you find the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.