Exploring Piecewise and Composite Functions

What is a piecewise function?

• A function that only uses positive numbers.

• A function that is always continuous.

• A function defined by multiple equations over different intervals.

• A function defined by a single equation.

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

• The function has a maximum at that point.

• The value is not included in the function.

• The value is included in the function.

• The function is undefined at that point.

When graphing the piecewise function y = x + 2 for x < 0 and y = 2x - 1 for x ≥ 0, what is the y-value when x = 0?

• 1

• 0

• -1

• 2

What is the domain of the piecewise function y = x + 2 for x < 0 and y = 2x - 1 for x ≥ 0?

• x < 0

• x ≠ 0

• x ≥ 0

• All real numbers

How do you find the composition of two functions, f(g(x))?

• Plug the output of g(x) into f(x).

• Subtract g(x) from f(x).

• Multiply the two functions together.

• Add the two functions together.

If g(x) = x + 1 and f(x) = 2x + 1, what is f(g(1))?

• 9

• 7

• 5

• 3

What is the result of g(f(3)) if f(x) = 2x + 1 and g(x) = (x + 1)^2?

• 49

• 100

• 81

• 64

What transformation occurs when f(x) is changed to f(x - c)?

• Shift down by c units

• Shift to the right by c units

• Shift up by c units

• Shift to the left by c units

What happens to the graph of f(x) when it is reflected across the x-axis?

• All positive y-values become negative y-values.

• The graph shifts to the right.

• All positive x-values become negative x-values.

• The graph shifts to the left.

If the original graph is f(x) and we want to move it up by c units, what transformation should we apply?

• f(x + c)

• f(x) + c

• f(x) - c

• f(x - c)