Graphing Logarithmic Functions | Summary and Q&A

TL;DR

Learn how to graph logarithmic functions and understand the four basic shapes they can take.

Key Insights

• 🚦 Logarithmic functions are the inverse of exponential functions and contain vertical asymptotes.
• 😥 Graphing logarithmic functions requires finding the vertical asymptote and plotting two points.
• ❣️ The four basic shapes of logarithmic functions determine the range of x and y values.
• ☠️ Logarithmic functions increase at a decreasing rate compared to exponential functions.
• 🤯 The domain and range of logarithmic functions are restricted, with the lowest x value being the vertical asymptote.
• ❣️ By analyzing the signs in front of x and y, you can determine the direction of the graph.
• 😥 The points on the graph of a logarithmic function will guide you in plotting the correct shape.

Transcript

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Questions & Answers

Q: What are logarithmic functions?

Logarithmic functions are the inverse of exponential functions. They represent the relationship between an exponent and a base, where the exponent is the logarithm of a given number to the base.

Q: How do logarithmic functions relate to exponential functions?

Logarithmic functions and exponential functions are inverse functions of each other. The graph of a logarithmic function is obtained by reflecting the graph of its corresponding exponential function across the line y = x.

Q: What are the four basic shapes of logarithmic functions?

The four basic shapes of logarithmic functions are: traveling towards quadrant one, reflecting across the y-axis, reflecting across the x-axis, and reflecting across the origin. Each shape represents different ranges of positive and negative x and y values.

Q: How do you graph a logarithmic function?

To graph a logarithmic function, first find the vertical asymptote by setting the inside of the logarithm equal to zero. Then choose two points and calculate their corresponding y values. Plot these points on the graph, starting from the vertical asymptote, to get the shape of the function.

Summary & Key Takeaways

• Logarithmic functions are the inverse of exponential functions and contain vertical asymptotes.

• There are four basic shapes of logarithmic functions: traveling towards quadrant one, reflecting across the y-axis, reflecting across the x-axis, and reflecting across the origin.

• To graph a logarithmic function, find the vertical asymptote, determine the x and y values for two points, and plot them on a graph.