Section 2.1 part 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

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

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

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

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

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

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

(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)

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 – 3 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)

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 – 8 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)

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

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)

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