How to find the domain and range of a piecewise function | Functions | Algebra I | Khan Academy

TL;DR

Analyzing the domain and range of a piecewise linear function through different intervals of x.

Transcript

So we have a piecewise linear function right over here for different intervals of x. g of x is defined by a a line or the line changes depending what interval of x we're actually in. And so let's think about its domain, and then we'll think about its range. So the domain of this, this is a review. The domain is the set of all inputs for which this ... Read More

Key Insights

• #️⃣ The domain of the function is all real numbers between and including -6 and 6.
• 🤯 The function is not defined for x values lower than -6.
• 🧡 The range of the function is between -3 and 4, including both values.
• 👈 The function hits its low point when x approaches -6 and its high point when x is equal to -3.

Questions & Answers

Q: What is the domain of the piecewise linear function?

The domain of the function is all real numbers such that x is greater than -6 and less than or equal to 6.

Q: Can the function take on the value of -3?

Yes, the function can take on the value of -3 when x is equal to 4.

Q: What is the lowest value the function can take on?

The lowest value the function can take on is -3.

Q: What is the highest value the function can take on?

The highest value the function can take on is 4.

Q: Is the function defined for x = -6?

No, the function is not defined for x = -6 or any value lower than -6.

Q: In which interval does the function hit its low point?

The function hits its low point when x is as small as possible, approaching -6.

Q: What is the maximum value of the function?

The maximum value of the function is 4 when x is equal to -3.

Q: Can the function take on values beyond 4?

Yes, the function can take on values greater than 4.

Summary & Key Takeaways

• The domain of the piecewise linear function is the set of all x values for which the function is defined. It is defined for all x greater than -6 and less than or equal to 6.

• The range of the function is the set of all values that the function can take on. It can take on values between and including -3 and 4.