Evaluating Piecewise Defined Functions

This video tutorial introduces piecewise defined functions, explaining their structure and how they are used to represent different rules for different parts of a domain. Using a real-world scenario of Armando's travel, the video demonstrates how to construct and evaluate piecewise functions. It covers the interpretation of graphs, calculation of slopes, and evaluation of function values for specific inputs, providing a comprehensive understanding of piecewise functions.

What is a piecewise defined function?

• A function that is only defined for negative values

• A function that is only defined for positive values

• A function that is defined by multiple rules over different parts of its domain

• A function with a single rule for its entire domain

Why can't we use a single function to graph Armando's trip?

• Because the trip is too short

• Because the trip involves different speeds and stops

• Because the trip is too long

• Because the trip is not linear

What is the rate at which Armando drives to the grocery store?

• 0.6 miles per minute

• 0.5 miles per minute

• 0.4 miles per minute

• 0.7 miles per minute

How long does Armando stop to buy snacks?

• 3 minutes

• 5 minutes

• 4 minutes

• 6 minutes

What is the slope of the graph when Armando drives to the soccer field?

• 0.8

• 0.5

• 0.6

• 0.7

What is the y-intercept for the last part of Armando's trip?

• 2.7

• 0

• -1.5

• -2.7

Which function should be used to evaluate f(-4) in the given piecewise function?

• The function for x less than 1

• The function for x greater than 1

• The function for x equal to 1

• The function for x greater than or equal to 1

What is f(1) in the given piecewise function?

• 1

• 2

• 4

• 3

Which section does x = 3.2 fall into in the second example?

• Red section

• Yellow section

• Green section

• Blue section

What is the value of f(6) in the second example?

• 24

• 12

• 6

• 36