Master

Domain and Range of Exponential and Logarithmic Functions

Master domain and range of exponential and logarithmic functions with interactive lessons and practice problems! Designed for students like you!

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Domain and Range of Exponential and Logarithmic Functions

Study Guide

Key Definition

The domain of a function is the set of input values for which the function is defined, while the range is the set of all output values the function takes. For exponential functions like $f(x) = 2^x$, the domain is all real numbers, but the range is $y > 0$.

Important Notes

Exponential functions like $f(x) = 2^x$ have domains of all real numbers.
The range of $f(x) = 2^x$ is $y > 0$.
Reflection over the x-axis changes the range of $-2^x$ to $y < 0$.
Logarithmic functions have domains $x > 0$.
The range of logarithmic functions is all real numbers.

Mathematical Notation

Remember to use proper notation when solving problems

Why It Works

Exponential functions grow rapidly based on their base value. Understanding their domain and range helps in graphing and interpreting their behavior over different intervals.

Remember

Exponential functions will never reach zero, and logarithmic functions cannot take negative or zero values as input.

Quick Reference

Exponential Function:$y = a^x$

Logarithmic Function:$y = \log_a(x)$

Understanding Domain and Range of Exponential and Logarithmic Functions

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with $y = 2^x$ and its domain and range.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the range of the function $f(x) = 2^x$?

Real-World Problem

Question Exercise

Intermediate

Bacteria Growth Scenario

Imagine a population of bacteria that doubles every hour. What is the population $P(t)$ as a function of time $t$?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the function $f(x) = \log_2(x)$. Determine the domain of this function.

Challenge Quiz

Single Choice Quiz

Advanced

Which transformation applies to the function $g(x) = 2^{-x}$ compared to $f(x) = 2^x$?

Recap

Watch & Learn

Review key concepts and takeaways