SOLUTION: #18 y=6 absolute value of x-7 it says to gragh the function, identify the vertex,whether it opens up or down,and whether the graph is wider, narrower, or the same width as the

Algebra ->  Absolute-value -> SOLUTION: #18 y=6 absolute value of x-7 it says to gragh the function, identify the vertex,whether it opens up or down,and whether the graph is wider, narrower, or the same width as the       Log On


   

Question 101003This question is from textbook algebra 2
: #18
y=6 absolute value of x-7
it says to gragh the function, identify the vertex,whether it opens up or down,and whether the graph is wider, narrower, or the same width as the graph of y= the absloute value of x
 This question is from textbook algebra 2

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The graphs that you are looking for are shown below. The red graph is the graph of y= 6|x-7| and
the green graph is the graph of y = |x|.
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Note that the red graph should be touching the x axis at the point x = 7. The graphing program
apparently has a little difficulty in showing it as it should be. You can tell that y should
be 0 when x is +7 by substituting +7 for x in the equation y = 6*|x-7|. When you substitute
+7 for x the terms +7 and -7 inside the absolute value signs cancel to make the equation be
y = 6*|0| and this reduces to y = 0.
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graph%28600%2C600%2C-10%2C20%2C-5%2C+25%2C+6%2Aabs%28x-7%29%2C+abs%28x%29%29
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So the vertex is at (+7,0). As you can see, the graph opens up. And the graph of y = 6*|x-7|
is narrower than the graph of y = |x|. This is because the absolute value quantity is
multiplied by 6, so for a given value of x from the vertex, it rises 6 times faster. To
demonstrate this we'll eliminate the multiplier of 6 and show the two graphs of y = |x-7| in
red and y = |x| in green. Notice that without the multiplier of 6 the red graph is the same
width as the green graph.
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graph%28600%2C600%2C-10%2C20%2C-5%2C+25%2C+abs%28x-7%29%2C+abs%28x%29%29
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Now that you have seen the graphs and have evaluated y when x equals +7 to find the vertex
point of (7, 0), you can get other points on the graph by just assigning x some values in
either direction from x = +7. For example, when x = 0, then y = 6*|0 - 7|, and the absolute
value signs make this equation become y = 6*+7 = 42. Therefore you know that the point (0, 42)
is on the graph. And when x = +5 then y = 6*|5 - 7| = 6*|-2| = 6*2 = 12. So you know the point
(5, 12) is on the graph. And when x = 8 then y = 6*|8 - 7| = 6*|-1| = 6*1 = 6. Therefore,
the point (8, 6) is on the graph. You can continue this to get a sufficient number of
points to allow you to draw the graph.
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Hope the graphs help you to see what is going on in the problem.
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