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 y = ab^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 increases or decreases rapidly.

Front

What does the slope (m) represent in the equation y = mx + b?

Back

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

Front

What does the y-intercept (b) represent in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x = 0. It is the point where the line crosses the y-axis.

Front

How do you determine if a function is linear or exponential from a table of values?

Back

If the differences between consecutive y-values are constant, the function is linear. If the ratios of consecutive y-values are constant, the function 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 formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does f(4) = 16 indicate in function notation?

Back

f(4) = 16 indicates that when the input x is 4, the output of the function f is 16.

Front

How do you write an equation for exponential decay?

Back

An equation for exponential decay can be written as y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Front

What is the difference between linear growth 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.