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

2. Homework Questions?

3. 3.4 Modeling with Functions
Water Under the Bridge
3.4 Modeling with Functions

4. Today’s Objectives
Use multiple representations of functions to model and solve problems .
Use multiple representations of functions to analyze problems .

5. 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

6. 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

7. 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 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.

8. Today’s Objectives
Use multiple representations of functions to model and solve problems .
Use multiple representations of functions to analyze problems .

9. 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.