Understanding Piecewise Functions

What is a piecewise function?

• A function that cannot be graphed

• A function composed of multiple sub-functions, each with its own domain

• A function defined by a single equation

• A function that only uses linear equations

How do you determine the domain of a piecewise function?

• By checking the slope of the function

• By looking at the y-values

• By evaluating the function at zero

• By considering the x-values and any restrictions

What is the range of a piecewise function?

• The set of all possible x-values

• The set of all possible y-values

• The difference between the highest and lowest y-values

• The set of all possible slopes

How do you evaluate a piecewise function at a specific point?

• By using the function with the highest degree

• By identifying which sub-function's domain includes the point and using that function

• By substituting the point into all functions and averaging the results

• By using the first function in the piecewise definition

If f(x) = x^2 for x ≥ 0, what is f(3)?

• 12

• 6

• 9

• 3

What types of functions can be part of a piecewise function?

• Only linear functions

• Any type of function, including linear, quadratic, and square root

• Only constant functions

• Only quadratic functions

In a piecewise function, what does an open circle on a graph indicate?

• The function is undefined at that point

• The point is not included in the function

• The point is included in the function

• The function has a maximum at that point

How do you combine multiple functions into a single piecewise function?

• By using only the function with the largest domain

• By defining each function over a specific domain

• By multiplying all the functions together

• By adding all the functions together

What is the domain of a piecewise function that includes a square root function starting at x > 1?

• x > 1

• x ≥ 0

• x < 1

• All real numbers

If a piecewise function has a constant function f(x) = 2 for x = 1, what is f(1)?

• 2

• 1

• 3

• 0