1. 1.6a Modeling with Functions!!!
The last section of the chapter!!!
Homework: p odd

2. Recall… Of course, our first task is to become
One of the main themes of Sec. 1.1 was to model
real-world situations in several different ways (e.g.,
numerically, graphically, etc.). We focus now on
using functions in models.
Of course, our first task is to become
experts at writing these functions…

3. Consider these problems…
Write an algebraic expression for the quantity described:
A number x increased by 5 and then tripled.
Four more than 5% of a number x.

4. Guided Practice Write the area of a circle as a function of its:
(a) radius r
(b) diameter d
(c) circumference C

5. Guided Practice
Write an algebraic expression for the quantity described:
The area of a triangle whose altitude is 2 more than its base
length x.
Income after a 3% drop in the current income of x dollars.

6. Guided Practice
Choose a variable and write a mathematical expression for the
quantity described verbally:
Total Cost: The total cost is $28,000 increased by 9% plus
$19.85 for each item produced.
Let C be the total cost and n be the number of items produced

7. Guided Practice
Choose a variable and write a mathematical expression for the
quantity described verbally:
Profit: The profit consists of a franchise fee of $200,000 plus
12% of all sales.
Let P be the profit and s be the amount of sales

8. Guided Practice
Write the specified quantity as a function of the specified
variable. In some cases, it may be helpful to draw a picture.
One leg of a right triangle is twice as long as the other. Write
the length of the hypotenuse as a function of the length of the
shorter leg. c x 2x

9. Guided Practice
Write the specified quantity as a function of the specified
variable. In some cases, it may be helpful to draw a picture.
A square is inscribed in a circle. Write the area of the square
as a function of the radius of the circle. 2r s s

10. An isosceles triangle has its base along the x-axis with one base
vertex at the origin and its vertex in the first quadrant on the
graph of Write the area of the triangle as a function
of the length of the base.