Math 4 Unit 2 Piecewise Functions-Flashcard -1A

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

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 a jump discontinuity?

Back

A jump discontinuity occurs when the left-hand limit and the right-hand limit at a 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.

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-intercept of a function?

Back

To find the x-intercept, set the function equal to zero and solve for x.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at a point if there is no valid output for that input, often due to division by zero or taking the square root of a negative number.

Front

Evaluate h(x) = { 2x + 1, x < 2; 3, x = 2; x^2 - 4, x > 2 } at x = 2.

Back

h(2) = 3.

Front

Evaluate h(x) = { 2x + 1, x < 2; 3, x = 2; x^2 - 4, x > 2 } at x = 1.

Back

h(1) = 2(1) + 1 = 3.

Front

Evaluate h(x) = { 2x + 1, x < 2; 3, x = 2; x^2 - 4, x > 2 } at x = 3.

Back

h(3) = 3^2 - 4 = 5.