Math assignment - Families of Functions.

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Erik Skyllberg                                                NEG

2003-04-03

Math assignment

Families of Functions

Linear Function:

A linear function is formed by the slope-intercept form y = mx + b, where m is the gradient/slope, and b is the y-intercept. The greater gradient, the steeper the line will be.

The gradient can be calculated through taking ∆y/∆x. Then you will have to use two points on each line.

The y-intercept of my first linear function graph, the red line, is 2, due to that b = 2. The gradient is + 3, which also can be written 3/1. To find out that, it is possible to use the rise/run method. That means that you already know one point on the graph, the y-intercept + 2. From that point you can go upwards (rise) three units, and one unit to the right (run). You could also use the ∆y/∆x method to calculate the gradient. Then you take two co-ordinates on the graph. In my example I have chosen to take (-1, -1) and (0,2). I then take (2-(-1)) / (0-(-1)) = 3/1 which gives me the same answer (y2-y1 / x2-x1).  

In my second linear function graph, the gradient is negative, which means that my line will be moving downwards from left to right. The y-intercept is – 4 and the gradient is – 2. To calculate the slope I use the co-ordinates (-2,0) and (-1, -2). I use the ∆y/∆x method once again. (-2-0) / (-1-(-2)) = -(2/1).

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Absolute Value Function:

In an absolute value function, the graph is determined from the sign that is before the absolute value signs, since what is inside always will be positive after removing the absolute value signs. The characteristics of an absolute value graph are that it is a V-shape, either positive that opens upwards, or negative that opens downwards, as shown in my examples. The function is often written Y = | x - b|. The vertex is (b, 0). Since the b is inside the absolute value symbols, it ...

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