Linear or Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 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. The graph of an exponential function shows rapid growth or decay.

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. This means that the difference in y-values divided by the difference in x-values will be the same for any two points.

Front

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

Back

An exponential function will show a constant multiplicative rate of change. This means that the ratio of consecutive y-values will be constant.

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 general form of an exponential equation?

Back

The general form of an exponential equation is y = a * b^x, where a is a constant, b is the base, and x is the exponent.

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 does the base of an exponential function represent?

Back

The base of an exponential function represents the growth factor. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis, which occurs when x = 0. It is represented by the value of b in the equation f(x) = mx + b.

Front

What is the domain of a linear function?

Back

The domain of a linear function is all real numbers, as linear functions are defined for every value of x.