1.7 Evaluate Piecewise Functions

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals of its domain.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which interval the point falls into and use the corresponding expression to find the function's value.

Front

What does f(3) = 5 indicate about the piecewise function?

Back

It indicates that when the input is 3, the output of the piecewise function is 5, meaning the expression for that interval yields 5.

Front

What is the significance of 'undefined' in piecewise functions?

Back

'Undefined' indicates that the function does not have a value at that specific input, often due to the input not falling within any defined interval.

Front

If f(-2) = 4, what can we infer about the piecewise function?

Back

We can infer that the expression for the interval containing -2 evaluates to 4.

Front

What does g(4) = -5 tell us about the function g?

Back

It tells us that for the input 4, the output of the function g is -5, indicating the specific expression used for that interval.

Front

How do you determine the output of a piecewise function for g(7)?

Back

To determine g(7), identify the interval that includes 7 and apply the corresponding expression to find the output.

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What is the output of f(0) if f(0) = 0?

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The output of f(0) is 0, meaning the function evaluates to 0 at the input of 0.

Front

What does it mean if multiple expressions are used in a piecewise function?

Back

It means that the function behaves differently in different intervals of its domain, allowing for more complex behavior.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval and ensure to indicate any points where the function is undefined.