Comparing Functions: Equations and Verbal Descriptions

This video tutorial teaches how to compare functions by analyzing equations and verbal descriptions. It introduces the four representations of functions: algebraic, graphic, numeric, and verbal. The tutorial provides real-world examples, such as selling programs and recycling cans, to illustrate how to translate verbal descriptions into equations. It emphasizes understanding function properties, such as one-to-one relationships and constant rates of change, and highlights common mistakes in interpreting verbal descriptions. The lesson concludes with a practical example of managing a lunch card balance.

What is a verbal description in the context of functions?

• A graphical representation of a function

• A numeric representation of a function

• An algebraic representation of a function

• A way to describe a function using words

If Mike sells programs at $2 each, what is the correct equation for the total cost?

• y = 2 + x

• y = x - 2

• y = 2 * x

• y = x + 2

What is the constant rate of change for California's recycling program?

• 20 cents per can

• 15 cents per can

• 5 cents per can

• 10 cents per can

How much does Michigan offer for each soda can recycled?

• 20 cents

• 10 cents

• 15 cents

• 5 cents

What indicates a constant rate of change in a verbal description?

• Words like 'sometimes' and 'occasionally'

• Words like 'never' and 'always'

• Words like 'for every' and 'each'

• Words like 'rarely' and 'seldom'

In the lunch card example, what is the constant rate of change?

• -$50 per month

• -$1.25 per lunch

• $1.25 per lunch

• $50 per month

What is the main takeaway from comparing functions using equations and verbal descriptions?

• Verbal descriptions are not useful for functions

• Functions can only be compared using graphs

• Equations are always more accurate than verbal descriptions

• Each input has a unique output in a function