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 parts of its domain.

Front

What does the domain of a function represent?

Back

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

Front

What does the notation x > 5 indicate about the domain?

Back

It indicates that the function is defined for all numbers greater than 5.

Front

What is the value of g(7) if g(x) = 2x - 3?

Back

g(7) = 2(7) - 3 = 14 - 3 = 11.

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, determine which piece of the function applies to the given input value and then use that piece to find the output.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does the notation 0 ≤ x < 2 indicate about the domain?

Back

It indicates that the function is defined for all numbers from 0 to 2, including 0 but not including 2.

Front

What is the value of m(-3) if m(x) = x + 6?

Back

m(-3) = -3 + 6 = 3.

Front

What is the significance of domain restrictions in piecewise functions?

Back

Domain restrictions limit the input values for which the function is defined, affecting the overall behavior of the function.

Front

What is f(-1) if f(x) = 2x - 4?

Back

f(-1) = 2(-1) - 4 = -2 - 4 = -6.