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

How can you identify an exponential function from a set of ordered pairs?

Back

An exponential function can be identified if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) are equally spaced.

Tags

CCSS.HSF-LE.A.1A

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where 'a' is the initial value and 'b' is the base of the exponential.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

Front

What does the y-intercept of a function represent?

Back

The y-intercept of a function is the value of the function when x = 0, representing the point where the graph intersects the y-axis.

Front

Given the ordered pairs (0, 1), (1, 4), (2, 16), (3, 64), what type of function is represented?

Back

The function represented by these ordered pairs is exponential.

Tags

CCSS.HSF-LE.A.1A

Front

What is the y-intercept of the function g(x) if g(0) = 1?

Back

The y-intercept of g(x) is 1.

Front

How do you determine if a function is linear based on ordered pairs?

Back

A function is linear if the differences between consecutive y-values are constant when the x-values are equally spaced.

Tags

CCSS.HSF-LE.A.1B

Front

What is the significance of the base 'b' in an exponential function?

Back

The base 'b' determines the growth or decay rate of the exponential function; if b > 1, the function grows, and if 0 < b < 1, the function decays.

Tags

CCSS.HSF-IF.C.8B

Front

What is an example of a real-world application of exponential functions?

Back

Exponential functions are used to model population growth, radioactive decay, and compound interest.