Understanding Piecewise Linear Functions

The video tutorial explains piecewise linear functions, focusing on their domain and range. It begins with an introduction to piecewise functions and their intervals. The domain is defined as the set of all x values for which the function is defined, specifically between -6 and 6. The range is discussed as the set of all possible output values, with g(x) ranging from -3 to 4. The tutorial provides a detailed analysis of how the function behaves across different intervals, emphasizing the importance of understanding both domain and range in piecewise functions.

What is a piecewise linear function?

• A function that is always increasing.

• A function that is not defined for any interval.

• A function defined by multiple linear equations over different intervals.

• A function defined by a single linear equation.

What is the domain of a function?

• The set of all possible inputs.

• The set of all possible intervals.

• The set of all possible equations.

• The set of all possible outputs.

For the given function, what is the lower bound of the domain?

• x is greater than or equal to 6

• x is less than or equal to 6

• x is greater than -6

• x is less than -6

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What is the range of a function?

• The set of all possible inputs.

• The set of all possible equations.

• The set of all possible outputs.

• The set of all possible intervals.

When does the function hit its lowest point in the first interval?

• When x is equal to 3

• When x is equal to 0

• When x is approaching 6

• When x is approaching -6

What is the maximum value of g(x) in the first interval?

• 6

• 4

• 3

• 1

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In the second interval, what is the minimum value that g(x) can approach?

• 4

• -3

• 0

• 1

What is the maximum value of g(x) in the second interval?

• 4

• 3

• 1

• 6

In the third interval, what is the maximum value of g(x)?

• -3

• 0

• 1

• 4

What is the range of g(x) for the entire function?

• g(x) is between 0 and 1

• g(x) is between 1 and 4

• g(x) is between -3 and 4

• g(x) is between -6 and 6