The animation is already done for you; just copy and paste the slide into your existing presentation.

6.6 Transforming Linear Functions Page 193

How are the changes to the parameters of a linear equation reflected in its graph?

New Vocabulary Family of functions – a set of functions whose graph have basic characteristics in common. (Example: y = x, y = x + 3, y = 2x - 5) Parent Function – the most basic function of a family of functions. (The parent function in the following group of functions y = x, y = x + 3, y = 2x - 5 is y = x) Parameter – one of the constraints in a function or equation that determines which variation of the parent function one is considering. (Example: For the function y = mx + b, the two parameters are m and b. The basic function is y = x. The slope, m, and the y-intercept, b, changes the slope and y-intercept of the parent function y = x.)

Explore Activity 1 Let’s investigate what happens to the graph of f(x) = x + b when you change the value of b.

Explore Activity 1 continued (Part B) Let’s look at the graph of f(x) = x. What is the slope and y-intercept?

Explore Activity 1 continued (Part C) Let’s graph another function and compare them. How are they alike? How are they different? This is called a vertical translation. All points on the line has moved up 2 units. f(x) = x f(x) = x + 2

Reflection Consider the graph f(x) = x + b. What happens to the graph when you increase the value of b? The graph is translated up. What happens to the graph when you decrease the value of b? The graph is translated down. f(x) = x f(x) = x + 2 f(x) = x - 2

Summary – Changing the value of b In summary, changing the value of the y-intercept translates the function vertically (either up or down).

Explore Activity 2 Let’s investigate what happens to the graph of f(x) = x + b when you change the value of m.

Explore Activity 2 continued (Part A) Let’s graph several functions and compare them. How are they alike? How are they different? As the value of m increases from 1, does the graph become steeper or less steep? f(x) = x f(x) = 2x f(x) = 6x

Explore Activity 2 continued (Part B) Let’s graph several functions and compare them. How are they alike? How are they different? As the value of m decreases from 1 to 0, does the graph become steeper or less steep? f(x) = x

Explore Activity 2 continued (Part C) Let’s look at another set of functions and compare them. How are they alike? How are they different? How are the graphs of f(x) = x and f(x) = -x geometrically related? They are reflections of each other over the x-axis and y-axis. f(x) = x f(x) = -x

Explore Activity 2 continued (Part D) Now we are going to compare the effect of changing the slope. What happens to the graph of f(x) = mx as the value of m decreases from -1 and as it increases from -1 to 0? f(x) = -x f(x) = -2x f(x) = -4x

Turn to page 195 Complete the table in number 8.

The answers are…