Exploring Piecewise Functions with Desmos

What is a piecewise function?

• A function that has no restrictions on its domain.

• A function defined by two or more equations, each applying to a different part of the domain.

• A function that is always linear.

• A function defined by a single equation.

In a piecewise function, what does a circle on the graph represent?

• The value is both included and not included.

• The value is not included in the function.

• The value is irrelevant.

• The value is included in the function.

How do you determine which equation to use when evaluating a piecewise function at a specific point?

• Use the first equation listed.

• Use the equation with the smallest coefficient.

• Use the equation with the highest degree.

• Use the equation that applies to the given x-value based on the domain restrictions.

What is the value of f(4) for the piecewise function defined as f(x) = x - 2 if x ≤ 0 and f(x) = 2x + 1 if x > 0?

• 3

• 5

• 9

• 7

When graphing a piecewise function in Desmos, what symbol is used to indicate a domain restriction?

• Quotation marks

• Parentheses

• Braces

• Brackets

What is the domain of the piecewise function y = -x - 4 if x < 0 and y = x if x ≥ 0?

• x < 0

• x = 0

• x ≥ 0

• All real numbers

How do you write the equation of a piecewise function from a graph?

• Use the same equation for all pieces.

• Only use the y-intercept.

• Ignore the domain restrictions.

• Identify the y-intercept and slope for each piece and determine the domain restrictions.

What is the slope of the line segment in the piecewise function f(x) = x + 3 if x < 0?

• 0

• 1

• 3

• -1

What does a step function graph look like?

• A parabola

• A circle

• A straight line

• A staircase

If a rental company charges $50 for the first day and $25 for each additional day, what is the cost for renting the item for 3 days?

• $150

• $125

• $100

• $75