Exploring Piecewise Functions and Their Transformations

What is a piecewise function?

• A function defined by a single equation.

• A function defined by multiple equations.

• A function that cannot be graphed.

• A function with no domain.

How do you find the value of a piecewise function at a specific point?

• By using the last equation in the function.

• By using the first equation in the function.

• By using the equation that corresponds to the given x-value.

• By averaging all the equations.

What is the domain of a piecewise function defined for all x greater than or equal to -3?

• (-∞, -3]

• (-3, ∞)

• [-3, ∞)

• (-∞, 3]

When graphing a piecewise function, what should you do?

• Graph only the last equation.

• Graph only the first equation.

• Graph each piece separately.

• Graph all equations on the same graph.

What happens to the graph of y = f(x) when you add a positive number C to the function?

• It shifts vertically up by C units.

• It shifts vertically down by C units.

• It shifts horizontally left by C units.

• It shifts horizontally right by C units.

What is the result of subtracting a positive number C from the function y = f(x)?

• The graph shifts vertically down by C units.

• The graph shifts horizontally right by C units.

• The graph shifts horizontally left by C units.

• The graph shifts vertically up by C units.

What is the effect of replacing x with x - H in the function y = f(x) when H is greater than zero?

• The graph shifts horizontally right by H units.

• The graph shifts vertically down by H units.

• The graph shifts horizontally left by H units.

• The graph shifts vertically up by H units.

How does the graph of y = f(x + H) change when H is greater than zero?

• It shifts vertically up by H units.

• It shifts vertically down by H units.

• It shifts horizontally right by H units.

• It shifts horizontally left by H units.

What happens to the graph of y = f(x) when it is multiplied by -1?

• It reflects about the y-axis.

• It reflects about the x-axis.

• It shifts vertically down.

• It shifts vertically up.

How do you reflect a function y = f(x) about the y-axis?

• Multiply the function by -1.

• Replace y with -y.

• Replace x with -x.

• Add a positive number to the function.