1. Section 2.1 part 2

2. On which interval is the function increasing?
Section 2.1 Topic: Increasing and Decreasing Functions
Example 1/ Graph the function f(x) = -x3 + 6x2 – 9x – 5 in the viewing rectangle [-3, 7, -15, 20] and find the following:
On which interval is the function increasing?
On which interval is the function decreasing?
Find any relative maxima
Find any relative minima

3. This can be represented by the following PIECEWISE FUNCTION:
Section 2.1 Topic: Piecewise Functions
Example 2
In a particular country, if your income is between 10,000 and 35,000 units (for a family of four), you are in Tax Bracket A. If your income is over 35,000 but less than or equal to 85,000 units, you are in Tax Bracket B. If your income is over 85,000 units but less than or equal to 200,000 units, you are in Tax Bracket C. If your income is over 200,000 units, you are in Tax Bracket D.
This can be represented by the following PIECEWISE FUNCTION:
f(x) =
Find the tax amount of someone who makes:
120,000 units
20,000 units
500,000 units

4. Graph the following piecewise function:
Section 2.1 Topic: Piecewise Functions
Example 3
Graph the following piecewise function:
f(x) =
Find the Domain of the piecewise function
Find the Range of the piecewise function

5. Graph the following piecewise function:
Section 2.1 Topic: Piecewise Functions
Example 4
Graph the following piecewise function:
f(x) =
Find the Domain of the piecewise function
Find the Range of the piecewise function

6. 3. or -4x > 36 Solve (interval notation) and graph:
GroupWork
Solve (interval notation) and graph:
6(3x – 4) – 11x > 10x + 3
-12 < < 9
or -4x > 36
4. Find the domain of y=

7. 5. Find where the function is increasing, decreasing, and
constant. Then find the domain and range:
6. Graph the following piecewise function:
f(x) =
Find the Domain of the piecewise function
Find the Range of the piecewise function

8. 4 Truths & a Lie
Write down 5 things about yourself – 4 true and 1 false
Write your name somewhere on the index card

9. (f + g)(x) = f(x) + g(x) (f – g)(x) = f(x) – g(x)
Section 2.2 Topic: Adding/Subtracting/Mult/Dividing Functions
(f + g)(x) = f(x) + g(x)
(f – g)(x) = f(x) – g(x)
(fg)(x) = f(x) · g(x)
(f/g)(x) = f(x) / g(x)

10. Evaluate the function if it exists. A) (f + g)(-3) B) (f – g)(1)
Section 2.2 Topic: Adding/Subtracting/Mult/Dividing Functions
Ex 1: f(x) = 2x2 – g(x) = x + 4
Evaluate the function if it exists.
A) (f + g)(-3)
B) (f – g)(1)
C) (fg)(-2)
D) (f/g)(-4)

11. Find (h + k)(-9), if it exists Find the domain of (h + k)(x)
Section 2.2 Topic: Adding/Subtracting/Mult/Dividing Functions
Ex 2: h(x) = x – k(x) =
Find (h + k)(-9), if it exists
Find the domain of (h + k)(x)
Find (k/h)(-7)
Find the domain of (h/k)(x)

12. B.) Find the domain of (f/k)(x)
Section 2.2 Topic: Adding/Subtracting/Mult/Dividing Functions
Ex 3: f(x) = 2x2 – 3x k(x) = 5x3
Find (f/k)(-2)
B.) Find the domain of (f/k)(x)

13. B) Find the domain of (f/g)(x)
Section 2.2 Topic: Adding/Subtracting/Mult/Dividing Functions
Ex 4: f(x) = ; g(x) =
Find (f/g)(x)
B) Find the domain of (f/g)(x)

14. The difference quotient is Find the difference quotient…
Section 2.2 Topic: The difference quotient
Example 5
The difference quotient is
Find the difference quotient…
a) for f(x) = 2x – 1
b) for f(x) = 3x2 – 5x + 4