Unit 3 Functions

Average Rate of Change: Increasing and Decreasing Functions 4.4 Average Rate of Change: Increasing and Decreasing Functions

Essential Question: How can I determine the average rate of a function?

Determine the Domain and Range f(x) = 2x2 + 3 Domain: x   Range: y ≥ 3 f(x) = |x + 3| Domain: x   Range: y ≥ 0 Domain: x ≥ 1 Range: y ≥ -2

Where is the graph increasing, decreasing or constant? Velocity (m/s) Time (seconds) 5 8

Where is the graph increasing, decreasing or constant? f(x) = x3 f(x) = x3 – 3x f(x) = x2 – 4x – 2

What does the slope represent? Average Velocity position (x1, f(x1)) (x0, f(x0)) time

Average Rate of Change Describes how much a nonlinear function changes over a given interval Used for function that model how quickly a given amount increase or decrease Example: Revenue Changes in temperatures Traveling speed Etc…

Average Rate of Change: Average Rate of Change between x = a and x = b:

Let f(x) = 3x2 – 2 Find Average Rate of Change [1, 7] Given: y = 1/2x2

Determine the Average Rate of change from 1991 to 1994 and compare it to the change from 1995 to 1997. Year Population 1990 624 1991 856 1992 1336 1993 1578 1994 1591 1995 1483 1996 994 1997 826 1998 801 1999 745 Sketch the graph, when is the function increasing or decreasing?

Example If an object is dropped from a height of 3,000ft, its distance above the ground after t seconds is given by the function h(t) = 3000-16t2. Find the object’s average speed for A) between 1.5 and 2.5 seconds B) between 5 and 10 seconds

Revisiting the Essential Question: How can I determine the average rate of a function?

Homework 4.4 Pg 245: 1 – 6, 16 – 26 even