Math 4 Unit 2 Piecewise Functions-Flashcard -2B

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

Evaluate the function f(x) = { -1 if x < 0, x^2 - 1 if 0 ≤ x < 3, 4 if x ≥ 3 } at x = 1.

Back

f(1) = 1^2 - 1 = 0.

Front

What is a removable discontinuity?

Back

A removable discontinuity occurs at a point where a function is not defined, but can be made continuous by defining it appropriately at that point.

Front

Evaluate the function f(x) = { 0 if x < 2, 3x - 6 if x ≥ 2 } at x = 2.

Back

f(2) = 3(2) - 6 = 0.

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

Evaluate the function f(x) = { x^2 - 4 if x < 2, 2x + 1 if x ≥ 2 } at x = 2.

Back

f(2) = 2(2) + 1 = 5.

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

Find x if h(x) = 0 for h(x) = { x^2 - 4 if x < 2, 2x - 4 if x ≥ 2 }.

Back

h(2) = 2(2) - 4 = 0, so x = 2.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x-values) for which the function is defined.

Front

Evaluate the function f(x) = { 3 if x < 1, x + 2 if 1 ≤ x < 4, 5 if x ≥ 4 } at x = 3.

Back

f(3) = 3 + 2 = 5.