Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped...
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Transcript of Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped...
![Page 1: Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x.](https://reader036.fdocuments.net/reader036/viewer/2022082517/56649d975503460f94a8045c/html5/thumbnails/1.jpg)
3.4 Absolute Value Functions
![Page 2: Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x.](https://reader036.fdocuments.net/reader036/viewer/2022082517/56649d975503460f94a8045c/html5/thumbnails/2.jpg)
Absolute Value is defined by:
0 xif x,-0 x if 0,0 xif x,
x
![Page 3: Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x.](https://reader036.fdocuments.net/reader036/viewer/2022082517/56649d975503460f94a8045c/html5/thumbnails/3.jpg)
The graph of this piecewise function consists of 2 rays, is V-shaped and opens up.
To the left ofx=0 the line isy = -x
To the right of x = 0 the line is y = x
Notice that the graph is symmetric in the y-axis because every point (x,y) on the graph, the point (-x,y) is also on it.
![Page 4: Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x.](https://reader036.fdocuments.net/reader036/viewer/2022082517/56649d975503460f94a8045c/html5/thumbnails/4.jpg)
y = a |x - h| + kVertex is at (h,k) & is symmetrical in the line
x=hV-shaped If a < 0 the graph opens down (a is negative)If a > 0 the graph opens up (a is positive)The graph is wider if |a| < 1 (fraction < 1)The graph is narrower if |a| > 1a is the slope to the right of the vertex(…-a is the slope to the left of the vertex)
![Page 5: Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x.](https://reader036.fdocuments.net/reader036/viewer/2022082517/56649d975503460f94a8045c/html5/thumbnails/5.jpg)
To graph y = a |x - h| + k1. Plot the vertex (h,k) 2. Set what’s in the absolute value
symbols to 0 and solving for x, gives you the x-coordinate of the vertex. The y-coordinate is k.
3. Use the slope to plot another point to the RIGHT of the vertex.
4. Use symmetry to plot a 3rd point5. Complete the graph
![Page 6: Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x.](https://reader036.fdocuments.net/reader036/viewer/2022082517/56649d975503460f94a8045c/html5/thumbnails/6.jpg)
Graph y = -|x + 2| + 31. V = (-2,3)2. Apply the
slope a=-1 to that point
3. Use the line of symmetry x=-2 to plot the 3rd point.
4. Complete the graph
![Page 7: Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x.](https://reader036.fdocuments.net/reader036/viewer/2022082517/56649d975503460f94a8045c/html5/thumbnails/7.jpg)
Graph y = -|x - 1| + 1
![Page 8: Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x.](https://reader036.fdocuments.net/reader036/viewer/2022082517/56649d975503460f94a8045c/html5/thumbnails/8.jpg)
Write the equation for:
![Page 9: Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x.](https://reader036.fdocuments.net/reader036/viewer/2022082517/56649d975503460f94a8045c/html5/thumbnails/9.jpg)
So the equation is:y = 2|x| -3
The vertex is at (0, -3)
The equation needs to be in the form
y = a | x – h | + k
Therefore, y = a | x – 0 | - 3
Find the slope to the right of the vertex to find ‘a’.
The equation is: y = 2 | x – 0 | - 3
![Page 10: Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x.](https://reader036.fdocuments.net/reader036/viewer/2022082517/56649d975503460f94a8045c/html5/thumbnails/10.jpg)
Write the equation for:
y = ½|x| + 3
![Page 11: Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x.](https://reader036.fdocuments.net/reader036/viewer/2022082517/56649d975503460f94a8045c/html5/thumbnails/11.jpg)
Assignment - Absolute Value Worksheet 1