Evaluating and Graphing Piecewise Functions

What is a piecewise function?

• A function defined by a single equation.

• A function that is always continuous.

• A function defined by multiple equations over different intervals.

• A function that only uses linear equations.

How do you determine which part of a piecewise function to use for a given x value?

• By using the part with the smallest coefficient.

• By using the part that is defined for the interval containing the x value.

• By using all parts and averaging the results.

• By using the part with the largest exponent.

What is f(-4) for the piecewise function defined as f(x) = x - 2 for x < 0 and f(x) = x^2 + 1 for x ≥ 0?

• 5

• 17

• -2

• -6

What is f(0) for the piecewise function defined as f(x) = x - 2 for x < 0 and f(x) = x^2 + 1 for x ≥ 0?

• 0

• -2

• 2

• 1

What does an open circle on a graph of a piecewise function indicate?

• The function has a maximum at that point.

• The point is included in the function.

• The point is not included in the function.

• The function is continuous at that point.

What is the value of f(3) for the piecewise function defined as f(x) = x - 2 for x < 0 and f(x) = x^2 + 1 for x ≥ 0?

• 7

• 10

• 12

• 9

In the graph of f(x) = x - 2 for x < 0, what is the y-coordinate of the point where x = -1?

• -1

• -2

• -3

• -4

For the function f(x) = 6 - x when x ≤ 3, what is the value of f(0)?

• 6

• 0

• 3

• 9

For the function f(x) = 3x - 6 when x > 3, what is the value of f(4)?

• 6

• 3

• 9

• 12

Why is it important to determine if a point is included or not in a piecewise function?

• To pass the vertical line test and ensure it is a function.

• To find the maximum value of the function.

• To ensure the function is continuous.

• To determine the slope of the function.