Graphing Exponential Functions With e, Transformations, Domain and Range, Asymptotes, Precalculus

TL;DR

Learn how to graph exponential functions and determine their domain and range using simple examples.

Transcript

in this video we're going to focus on graphing exponential functions including functions with base e but we'll cover that later in the video so let's start with a simple function y is equal to 2 raised to the x power how can we graph this particular function what would you do to graph it the best thing to do is to make a table and you want to plug ... Read More

Key Insights

• 😥 Graphing exponential functions involves creating a table of values and connecting the points.
• 🍉 The horizontal asymptote can be shifted up or down based on a constant term.
• ♾️ The domain of all exponential functions is from negative infinity to infinity.
• 🤪 The range of an exponential function starts from the horizontal asymptote and goes up to positive infinity, excluding the asymptote value.
• ⚾ The base of an exponential function, even when it's e, follows the same graphing rules.
• 🤘 The exponentials function's graph can reflect over the horizontal asymptote if there is a negative sign in front of it.
• ❣️ The domain represents all possible x values, while the range represents all possible y values of the function.

Questions & Answers

Q: How can I graph an exponential function?

To graph an exponential function, create a table by plugging in values and plot the corresponding points. Connect the points to form the graph.

Q: How does a constant term affect the horizontal asymptote?

A constant term shifts the horizontal asymptote up or down. If the constant is positive, the asymptote shifts up. If it's negative, the asymptote shifts down.

Q: What is the domain of an exponential function?

The domain of any exponential function is always from negative infinity to infinity. There are no restrictions on the values of x that can be plugged in.

Q: How do I determine the range of an exponential function?

The range of an exponential function depends on the horizontal asymptote. It starts from the asymptote and goes up to positive infinity, excluding the asymptote value itself.

Summary & Key Takeaways

• To graph exponential functions, create a table by plugging in values and plot the corresponding points.

• The horizontal asymptote of an exponential function can be shifted up or down based on a constant term.

• The domain of any exponential function is always from negative infinity to infinity, while the range depends on the horizontal asymptote.