Graphing Piecewise Functions: Day 2 Insights

What is a piecewise function?

• A function defined by multiple expressions over different intervals.

• A function that is always linear.

• A function defined by a single expression.

• A function that has no defined intervals.

In the given real-life example, what is the cost per pound for a package weighing between 2 and 10 pounds?

• $1.50 per pound

• $2.00 per pound

• $3.00 per pound

• $4.00 per pound

What does the curly brace in the function notation of a piecewise function indicate?

• That the function is quadratic.

• That the function is defined by multiple expressions.

• That the function is linear.

• That the function is undefined.

When graphing the piecewise function y = 2x - 1 for x < -2, what is the starting point?

• (-1, -4)

• (-3, -7)

• (-2, -5)

• (-2, -3)

What type of line segment is formed when x is between -2 and 1 for the function y = x + 5?

• A ray

• A segment

• A curve

• A parabola

Why is it important to avoid overlapping pieces in a piecewise function?

• To ensure the function is continuous.

• To avoid failing the vertical line test.

• To make the function quadratic.

• To simplify the function.

In the second example, what is the y-coordinate when x is -3 for the function y = -3/4x + 3?

• 2.75

• 3.25

• 4.75

• 5.25

What is the correct symbol for the interval when x is greater than 2 but less than or equal to 5?

• 2 < x < 5

• 2 ≤ x < 5

• 2 ≤ x ≤ 5

• 2 < x ≤ 5

In the final example, what is the y-coordinate when x is -6 for the function y = 1/3x - 1/2?

• -2.5

• -1.5

• -4.5

• -3.5

What type of line is formed by the function y = 5 in the final example?

• A curved line

• A diagonal line

• A horizontal line

• A vertical line