Illustrative mathematics algebra 1 unit 4 answer key pdf

This lesson enables students to experience the idea of a distance function before they learn about such functions more formally. The function comes up naturally in the context of computing absolute errors, so the lesson is built around the idea of guessing a target number and examining how far the guesses are from it.

Advanced preparation is required for this lesson. See Required Preparation.

Students guess the number of objects in a container, such as the one shown here. When given the actual number of items (47 snap cubes in the jar in this picture), they calculate the absolute guessing errors of everyone's guesses.

After plotting the absolute guessing errors as a function of the guesses, students notice that the points on the scatter plot form a V shape above the horizontal axis.

Students consider possible reasons for this and think about whether this behavior is generalizable to other guessing cases, regardless of the target number being guessed. They use their observations to make sense of absolute value functions in the next lesson.

Technology isn't required for this lesson but consider making it available, as there are opportunities for students to choose to use appropriate technology to solve problems (MP5), or for the class to process the collected data more efficiently.

The blackline master for the warm-up activity, which includes two tables and two blank coordinate planes, will be used throughout the lesson.

Problem 1

Match each equation with a description of the function it represents.

1:

To get the output, add 4 to the input, then multiply the result by 2.

2:

To get the output, add 2 to the input, then multiply the result by 4.

3:

To get the output, multiply the input by 2, then add 4 to the result.

4:

To get the output, multiply the input by 4, then add 2 to the result.

Problem 2

Function \(P\) represents the perimeter, in inches, of a square with side length \(x\) inches.

1. Complete the table. \(x\)\(P(x)\)

   0	1	2	3	4	5	6

2. Write an equation to represent function \(P\).

3. Sketch a graph of function \(P\).

Problem 3

Functions \(f\) and \(A\) are defined by these equations. 

\(f(x)=80-15x\)

\(A(x)=25+10x\)

 Which function has a greater value when \(x\) is 2.5?

Problem 4

An equilateral triangle has three sides of equal length. Function \(P\) gives the perimeter of an equilateral triangle of side length \(s\).

1. Find \(P(2)\)
2. Find \(P(10)\)
3. Find \(P(s)\)

Problem 5

Imagine a situation where a person is using a garden hose to fill a child's pool. Think of two quantities that are related in this situation and that can be seen as a function. 

1. Define the function using a statement of the form “\(\underline{\hspace{0.5in}}\) is a function of \(\underline{\hspace{0.5in}}\). Be sure to consider the units of measurement.

2. Sketch a possible graph of the function. Be sure to label the axes.

   Then, identify the coordinates of one point on the graph and explain its meaning.

Problem 6

Function \(C\) gives the cost, in dollars, of buying \(n\) apples. 

Which statement best represents the meaning of \(C(10)=9\)?

A:

The cost of buying 9 apples

B:

The cost of 9 apples is $10.

Problem 7

Diego is baking cookies for a fundraiser. He opens a 5-pound bag of flour and uses 1.5 pounds of flour to bake the cookies.

Which equation or inequality represents \(f\), the amount of flour left in the bag after Diego bakes the cookies?