Math 4 Unit 2 Piecewise Functions-Flashcard -3B - Makeup

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 is a discontinuity in a function?

Back

A discontinuity in a function is a point at which the function is not continuous, meaning there is a break, jump, or hole in the graph.

Front

What is a jump discontinuity?

Back

A jump discontinuity occurs when the left-hand limit and right-hand limit of a function at a certain point exist but are not equal.

Front

What is a removable discontinuity?

Back

A removable discontinuity occurs when a function is not defined at a point, but the limit exists at that point, allowing the function to be 'fixed' by defining it at that point.

Front

What is an infinite discontinuity?

Back

An infinite discontinuity occurs when the function approaches infinity or negative infinity as it approaches a certain point.

Front

How do you find the x-value for a given f(x) value using a graph?

Back

To find the x-value for a given f(x) value, locate the horizontal line at that f(x) value and determine where it intersects the graph.

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 as x approaches that point equals the function's value at that point.

Front

Evaluate the piecewise function at x = 3: f(x) = { -3 if x < 2, 2 if x = 2, 5 if x > 2 }

Back

f(3) = 5.

Front

Evaluate the piecewise function at x = 2: f(x) = { -3 if x < 2, 2 if x = 2, 5 if x > 2 }

Back

f(2) = 2.