Evaluating and Graphing Piecewise Linear Functions

What defines a piecewise linear function?

• A function with a single formula for all values of x.

• A function with different formulas for different intervals of its domain.

• A function that can only have linear components.

• A function that is always continuous.

How do you evaluate f(9) for a piecewise linear function given its graph?

• By determining the slope at x=9.

• By calculating the area under the curve up to x=9.

• By finding the y-intercept of the graph at x=9.

• By locating the point on the graph where x=9 and finding its corresponding y value.

What is the significance of a 'filled in' point on a graph of a piecewise function?

• It is used to indicate a discontinuity.

• It signifies that the value at that point is included in the function.

• It represents an undefined value.

• It indicates the start of a new formula.

How do you derive the equation for a line segment in a piecewise function?

• By using the Pythagorean theorem.

• By using the slope-intercept form and identifying the slope and y-intercept from the graph.

• By calculating the derivative of the function.

• By integrating the function over the desired interval.

What method is suggested for graphing a piecewise linear function?

• Using a table of values.

• Plotting points and connecting them with solid lines immediately.

• Drawing the lines with dashed lines first, then making them solid over the relevant intervals.

• Graphing only the positive or negative parts first.

What is the purpose of using dashed lines when graphing a piecewise function?

• To highlight the discontinuities of the function.

• To represent the maximum and minimum values of the function.

• To show where the function is undefined.

• To indicate the parts of the graph that are not part of the function.

Why might a piecewise function be discontinuous at certain points?

• Because it changes formulas at those points.

• Because it cannot have negative values.

• Because it is not defined for those x values.

• Because all piecewise functions are discontinuous.

How can a piecewise function be continuous at a point where the formula changes?

• If the function has a vertical line at that point.

• If both formulas give the same output at that point.

• If the function is not defined at that point.

• If the point is an outlier.

What is the slope of a line segment that goes through the diagonals of the boxes and is decreasing?

• Undefined

• 1

• -1

• 0

In real-world applications, how are piecewise linear functions typically used?

• To simplify complex non-linear functions.

• To represent functions with only positive values.

• To calculate exact areas under curves.

• To model situations where a single formula cannot describe the entire scenario.