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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    |dw:1442374334038:dw|

  2. anonymous
    • one year ago
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    i know the answer i just need to know how to do it please

  3. anonymous
    • one year ago
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    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.

  4. anonymous
    • one year ago
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    you copy and pasted this

  5. anonymous
    • one year ago
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    yea i did

  6. anonymous
    • one year ago
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    https://au.answers.yahoo.com/question/index?qid=20110704084502AArYawN

  7. anonymous
    • one year ago
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    thats not helpful

  8. anonymous
    • one year ago
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    well i believe that explains pretty well

  9. anonymous
    • one year ago
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    i dont get it

  10. anonymous
    • one year ago
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    i dont see what else i can add

  11. anonymous
    • one year ago
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    so lost

  12. phi
    • one year ago
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    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

  13. phi
    • one year ago
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    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

  14. anonymous
    • one year ago
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    hmmmm this is pretty difficult but I think i kinda get it now

  15. phi
    • one year ago
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    what part is fuzzy?

  16. anonymous
    • one year ago
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    The part about the steepness of the slope and what it has to do with the given answers.

  17. phi
    • one year ago
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    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

  18. anonymous
    • one year ago
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    oh wait i re-read your explanation up there a couple times and now i got it lolol

  19. phi
    • one year ago
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    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)

  20. anonymous
    • one year ago
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    Yea I see now why it's choice D. Thanks phi you're the best!

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