Linear, Quadratic, Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What characterizes exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases over time.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How can you identify an exponential function from its equation?

Back

An exponential function can be identified by the variable being in the exponent, such as in f(x) = a * b^x.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the exponent is greater than 1, while exponential decay occurs when the base is between 0 and 1.

Front

What does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises steeply as x increases, starting from a point above the x-axis.

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function decreases rapidly and approaches the x-axis but never touches it.

Front

What is the y-intercept of the function f(x) = 2(3)^x?

Back

The y-intercept is 2, which occurs when x = 0.

Front

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

Back

You can determine the type of function by examining its equation: linear has no exponents on x, quadratic has x^2, and exponential has x in the exponent.