How To Find The Range of a Function

TL;DR

Understanding how to find the range of different functions based on their graphs and leading terms.

Transcript

in this video we're going to talk about how to find a range of a function so let's start with a linear function y equals x plus 3. the first thing that i would recommend doing is graphing a function so basically this graph is a straight-line graph but shifted up three units so the y-intercept is at three so this is a rough sketch of the graph let's... Read More

Key Insights

• ♾️ Linear functions have a range of negative infinity to infinity.
• 🥺 Quadratic functions with positive leading terms have a range from zero to infinity.
• ❎ Quadratic functions with negative leading terms have a range from negative infinity to a certain value.
• 🧡 Absolute value functions have a range that varies based on shifts and signs.
• 🧡 Radical functions have different ranges depending on shifts and signs.
• 🧡 Understanding how to graph functions helps in determining their range.
• ♾️ Continuous functions have a range from negative infinity to positive infinity.

Questions & Answers

Q: How do you find the range of a linear function?

To find the range of a linear function, look at the y-values on the graph. The range will be from negative infinity to positive infinity.

Q: How does the range of a quadratic function with a positive leading term differ from one with a negative leading term?

A quadratic function with a positive leading term has a range from zero to infinity, while a quadratic function with a negative leading term has a range from negative infinity to a certain value.

Q: How does the range of an absolute value function change with shifts and signs?

The range of an absolute value function depends on shifts and signs. A positive outside the absolute value function opens the graph upward, while a negative opens it downward. Shifts can change the lowest and highest y-values.

Q: How do you determine the range of a radical function?

To find the range of a radical function, analyze the shifts and signs. Positive inside and positive outside open the graph upward, while negative inside and positive outside open it downward. The lowest and highest y-values vary based on the shifts.

Summary & Key Takeaways

• Linear functions have a range of negative infinity to infinity, while quadratic functions with positive leading terms have a range from zero to infinity.

• Quadratic functions with negative leading terms have a range from negative infinity to a certain value, and absolute value functions can have a range that varies depending on the shifts and signs.

• Radical functions can have different ranges based on the shifts and signs.