anonymous
  • anonymous
Please Help ..... The figure shows the graph of the function f, defined by f(x)= |2x|+4 for all numbers x. For which of the following functions g, defined for all numbers x, does the graph of g intersect the graph of f? A. g(x)= x-2 B. g(x)= x+3 C. g(x)= 2x-2 D. g(x)= 3x-2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1442374334038:dw|
anonymous
  • anonymous
i know the answer i just need to know how to do it please
anonymous
  • anonymous
I think a quick way to get the answer is to notice that the slope of f(x) = 2x + 4 is 2, while the slope of f(x) = -2x + 4 is -2. Since f(x) = |2x| + 4 is basically a composite of these functions, the new f(x) is either increasing with slope 2 or decreasing with slope -2. To have a new linear function g(x) that is sure to intersect this function, the linear function has to be even steeper than this function, i.e. slope < -2 or slope > +2. Of your five choices, the only one meeting this requirement is E.

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anonymous
  • anonymous
you copy and pasted this
anonymous
  • anonymous
yea i did
anonymous
  • anonymous
https://au.answers.yahoo.com/question/index?qid=20110704084502AArYawN
anonymous
  • anonymous
thats not helpful
anonymous
  • anonymous
well i believe that explains pretty well
anonymous
  • anonymous
i dont get it
anonymous
  • anonymous
i dont see what else i can add
anonymous
  • anonymous
so lost
phi
  • phi
the slope of a line tells you how "steep" it is. if the slope is a big number, it would be harder to walk up it. from your graph |dw:1442413792486:dw| we should get the idea that some lines are too flat to ever intersect (meet) the red line
phi
  • phi
if that makes sense, then the next step is to figure out what is "too flat" or how steep does the line have to be ? we know that lines with the same slope are parallel to each other parallel means they never meet. y= |2x| +4 for x>=0 we can drop the | | (they make the inside positive, but for x>0 it already is positives so the absolute value does nothing) so for x>=0 y= 2x+4 any line with a slope of 2 will be parallel to this line. Choice C is C. g(x)= 2x-2 that has slope =2. so that line never meets the y=2x+4 line choices A and B have slopes of 1 and their y-intercepts are below the line in the graph. so those lines have a slope that is too flat. only choice D has a steep slope = 3 that is bigger than 2
anonymous
  • anonymous
hmmmm this is pretty difficult but I think i kinda get it now
phi
  • phi
what part is fuzzy?
anonymous
  • anonymous
The part about the steepness of the slope and what it has to do with the given answers.
phi
  • phi
do you have paper and a ruler? draw a V shape like in your graph. now put the ruler below the V and draw a "flat line" If you do that, you should see that the flat line will not meet the V now make the ruler a little more steep , and draw another line if you keep doing that, at some point, the line you draw will meet the V
anonymous
  • anonymous
oh wait i re-read your explanation up there a couple times and now i got it lolol
phi
  • phi
once you get the idea, you next need to look at an equation of a line and see which equation has a slope bigger than 2 (which is the slope of the V)
anonymous
  • anonymous
Yea I see now why it's choice D. Thanks phi you're the best!

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