Graphing+Linear+Functions-Target+E-Compare+It-Guided+Learning

Graphing Linear Functions-Target E: Graph and compare linear functions.

 * [[image:Discuss this.png width="173" height="97"]] || Sadie thinks that a horizontal shift and a vertical shift for a linear function are the same thing. Kari disagrees. Whom do you agree with and why? ||

Try exploring the effects of changing the slope (m) and y-intercept (b) of a linear function as compared to the parent (reference) function: //f//(//x//) = //x//.

The parent function, //y// = //x// (or //y// = 1//x//+0), is graphed below and represented by the dotted black line.

Use the sliders to change the values of m and b in the linear equation shown.

First, use the sliders to create the parent function, //y// = //x// (Click on the red circle of the slider and use the arrow keys to move). Next, systematically explore the lines that are created by changing the values of //** m **// and **// b //**. How does each compare to the parent function, //y// = //x//? How does //** m **// affect the graph? How does //** b **// affect the graph? media type="custom" key="27849963"

As you work through the applet, think about and answer the following questions:
 * If you change //**m**// to a number greater than 1, what happens to the graph?
 * If you change //**m**// to a negative, what happens to the graph?
 * If you change //**m**// to 1/2, what happens to the graph?
 * If you make //**b**// a 2, what happens to the graph?
 * If you make //**b**// a -4, what happens to the graph?

In order to describe the changes that occur to the graph, specific language needs to be used.

//y// = m//x// + b

To describe the changes in the slope (m) use the following:

Anytime the slope is positive, the graph of the function is INCREASING :


 * m > 1: the graph of the function is increasing more quickly
 * 0 < m < 1: the graph of the function is increasing more slowly

Anytime the slope is negative, the graph of the function is DECREASING :
 * -1 < m < 0: the graph of the function is decreasing more slowly
 * m < -1: the graph of the function is decreasing more quickly

To describe the changes in the y-intercept (b) use the following:
 * b is positive: the graph of the function translates (shifts) up "b units"
 * b is negative: the graph of the function translates (shifts) down "b units"

Sketch and describe how the graphs of the following functions compare to the graph of the parent function f(x) = x. Example 1: math h(x)=\frac{1}{4}x-1\ math

The graph of the function h(//x//) is: as compared to the parent function f(x). The sketch of the functions are below
 * increasing more slowly because m = 1/4
 * translated down 1 units because b = -1

Example 2 g(//x//) = -2//x// + 3

The graph of the function g(//x//) is: as compared to the parent function f(//x//). The sketch of the functions are below.
 * decreasing more quickly because m = -2
 * translated up 3 units because b = + 3




 * Graphing Linear Functions-Target E-Compare It-Quick Check**

Graph and Compare r(//x//) = -x - 4 to the parent function.

Graphing Linear Functions-Target E-Compare It-Quick Check Solutions