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 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.

Front

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

Back

A function is linear if it has a constant rate of change (the slope is constant). It is exponential if it has a variable rate of change (the growth or decay rate changes).

Front

What is the slope in a linear function?

Back

The slope (m) in 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 y-intercept represent in a linear function?

Back

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

Front

Given f(x) = -4x - 10, what is the value of f(0)?

Back

f(0) = -10.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

What is the value of f(10) for the function f(x) = 2x + 15?

Back

f(10) = 2(10) + 15 = 35.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(t) = a * e^(-kt), where a is the initial amount, k is the decay constant, and t is time.

Front

If a function doubles every year, what type of function is it?

Back

It is an exponential function.