Evaluating 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 then use the corresponding expression to find the function's value.

Front

What does it mean for a function to be continuous at a point?

Back

A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point.

Front

What is the significance of the domain in piecewise functions?

Back

The domain of a piecewise function specifies the intervals over which each piece of the function is valid.

Front

Evaluate f(-3) for the piecewise function defined as: f(x) = { -7 if x < -2, 4 if -2 ≤ x < 0, 18 if x ≥ 0 }

Back

f(-3) = -7.

Front

Evaluate f(0) for the piecewise function defined as: f(x) = { -3 if x < -2, 4 if -2 ≤ x < 0, 18 if x ≥ 0 }

Back

f(0) = 4.

Front

Evaluate f(12) for the piecewise function defined as: f(x) = { -19 if x < -10, 2 if -10 ≤ x < 15, 29 if x ≥ 15 }

Back

f(12) = 2.

Front

Evaluate f(-2) for the piecewise function defined as: f(x) = { -3 if x < -2, -2 if -2 ≤ x < 0, -1 if x ≥ 0 }

Back

f(-2) = -3.

Front

What is the formula for finding the limit of a piecewise function?

Back

The limit of a piecewise function at a point is found by evaluating the limit from the left and the right and checking if they are equal.

Front

What is a common mistake when evaluating piecewise functions?

Back

A common mistake is to use the wrong piece of the function for a given input, often due to misreading the intervals.