We are limited, but we can push back the border of our limitations.

Do Now

Take a square of graph paper from the shelf

Take out your student text book

Put your homework on your table for a stamp

1. The table of values shown describes a function.

a. Represent the table of values using an equation.

b. Write the equation using function notation.

c. Create a graph on the coordinate plane.

Homework Questions?

S

Water Under the Bridge

3.4 Modeling with Functions

Today’s Objectives

Use multiple representations of functions to model and solve problems .

Use multiple representations of functions to analyze problems .

The Water’s 5ft High and Rising

A nearby town hired a civil engineer to rebuild their storm drainage system . The drains in this town are open at the top to allow water to flow directly into them . While designing the drains, the engineer must keep in mind the height and the width of the drain . She needs to consider the height because the water cannot rise above the drain or it will flood the town and cause major destruction . However the drain must also be wide enough that it will not get clogged by debris .

The civil engineer will use rectangular sheets of metal to build the drains . These sheets are bent up on both sides to represent the height of the drain . An end view of the drain is shown .

Answer #1 with a partner

The Water’s 5ft High and Rising

Work on #2-5 with your partner

Paragraph at top of pg 160

#6-7 as a class

#8-11 with a partner

#12 with a partner

Determine the Best Design

A civil engineering company is hired to design a new drainage system for your town. To construct one of the storm drains, a sheet of metal that is 15.25 feet wide is folded on both sides.

Describe the drain that has the maximum cross-sectional area. Include at least two different representations in your description. Show all work and explain your reasoning.

Today’s Objectives

Use multiple representations of functions to model and solve problems .

Use multiple representations of functions to analyze problems .

3.4 Exit Slip

A rain gutter is to be constructed with a cross section that is a rectangle. The gutter is to be constructed out of a sheet of metal 15 inches wide.

1. Draw a diagram of this situation. Let x represent the height of the rain gutter.

2. Suppose the height of the rectangle is 4 inches. Determine the width of the rain gutter. Determine the area of the cross-section.