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anonymous

  • one year ago

Given the function f(x) = -2 |x-5/2|+6 and the graph g(x) shown below, over what interval do the functions f(x) and g(x) have the same minimum value? (Since I cannot graph g(x), its equation is 2|x+0.5| -3 ) @amistre64 @whpalmer4

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  1. amistre64
    • one year ago
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    what does it mean to have the same minimum value?

  2. anonymous
    • one year ago
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    No idea. xD

  3. amistre64
    • one year ago
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    well, it can mean 2 things to me ... what are your thoughts?

  4. anonymous
    • one year ago
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    I'm assuming it means the smallest value where they intersect

  5. amistre64
    • one year ago
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    that was one idea, does f(c) = g(c) ?? this doesnt sit right to me tho. given an interval x = [a,b] f and g have a minimum value within it such that say f(c) = g(d)

  6. amistre64
    • one year ago
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    |dw:1443371069792:dw|

  7. amistre64
    • one year ago
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    if we have this sort of interval, then we see we have 2 different minimums |dw:1443371139444:dw|

  8. amistre64
    • one year ago
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    what are our vertexes?

  9. amistre64
    • one year ago
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    and do we have options since there are about an infinite number of intervals we can make that satisfy the results...

  10. anonymous
    • one year ago
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    Im lost xd

  11. amistre64
    • one year ago
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    what is our vertex of g?

  12. anonymous
    • one year ago
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    The answer choices are A [0,8] B [1,7] C [-2,5] D [-5,1] E None of these

  13. amistre64
    • one year ago
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    |dw:1443371398297:dw| oh good, choices, then we have something we can compare

  14. amistre64
    • one year ago
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    what is our vertex of g, our biggest interval will then be along the y= axis of that vertex

  15. anonymous
    • one year ago
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    -.5,3?

  16. amistre64
    • one year ago
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    2|x+0.5| -3 ) -0.5, -3 is what it looks like to me, so when does f=-3?

  17. anonymous
    • one year ago
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    Not sure

  18. amistre64
    • one year ago
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    you have to solve for it ... -2 |x-5/2|+6 = -3 -2 |x-5/2| = -3-6 |x-5/2| = (3+6)/2 etc ...

  19. anonymous
    • one year ago
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    Ok so what would that be?

  20. amistre64
    • one year ago
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    im not going to do the algebra for you ...

  21. anonymous
    • one year ago
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    xd ok bare with my laziness gimme a sec

  22. anonymous
    • one year ago
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    x = -2 and x = 7?

  23. amistre64
    • one year ago
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    good, so this gives us the largest interval that the minimum of f and g are the same. any option of x < -2 is bad, and any option of x>7 is bad ... can we rule any out?

  24. amistre64
    • one year ago
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    outside of -2 to 7, the min of f drops below the min of g .... g cant go lower than its vertex by default

  25. anonymous
    • one year ago
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    I can rule D out

  26. amistre64
    • one year ago
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    D is bad, and A goes to 8 so it is bad for us too

  27. anonymous
    • one year ago
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    So is the answer none of these?

  28. amistre64
    • one year ago
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    |dw:1443372355236:dw|

  29. amistre64
    • one year ago
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    now, if our interval does NOT include -0.5, then it cannot include -2 or 7 but our only options left have -2 or 7 involved. which one does not contain x=-0.5?

  30. anonymous
    • one year ago
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    So it's none of these?

  31. amistre64
    • one year ago
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    you havent answered my question ...

  32. anonymous
    • one year ago
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    All of them?

  33. amistre64
    • one year ago
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    if your not understanding what I am asking for, then say so ...

  34. anonymous
    • one year ago
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    Yeah what are you trying to ask?

  35. amistre64
    • one year ago
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    im asking for an interval which contains x=-0.5 draw me a number line, -2 to 7 .. and tic off -0.5 for me

  36. anonymous
    • one year ago
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    |dw:1443372753726:dw|

  37. amistre64
    • one year ago
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    now show me on that drawing, where 1 to 7 fits in ..

  38. anonymous
    • one year ago
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    |dw:1443372851792:dw|

  39. amistre64
    • one year ago
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    |dw:1443372874804:dw| is -0.5 in the interval from 1 to 7?

  40. anonymous
    • one year ago
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    n0pe.

  41. amistre64
    • one year ago
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    is -0.5 in the interval from -2 to 5?

  42. anonymous
    • one year ago
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    yes

  43. amistre64
    • one year ago
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    then we should pick that one.

  44. anonymous
    • one year ago
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    So the answer is C?

  45. amistre64
    • one year ago
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    i would go with C yes

  46. anonymous
    • one year ago
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    Gracias!

  47. amistre64
    • one year ago
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    de nada

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