anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
what does it mean to have the same minimum value?
anonymous
  • anonymous
No idea. xD
amistre64
  • amistre64
well, it can mean 2 things to me ... what are your thoughts?

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anonymous
  • anonymous
I'm assuming it means the smallest value where they intersect
amistre64
  • amistre64
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)
amistre64
  • amistre64
|dw:1443371069792:dw|
amistre64
  • amistre64
if we have this sort of interval, then we see we have 2 different minimums |dw:1443371139444:dw|
amistre64
  • amistre64
what are our vertexes?
amistre64
  • amistre64
and do we have options since there are about an infinite number of intervals we can make that satisfy the results...
anonymous
  • anonymous
Im lost xd
amistre64
  • amistre64
what is our vertex of g?
anonymous
  • anonymous
The answer choices are A [0,8] B [1,7] C [-2,5] D [-5,1] E None of these
amistre64
  • amistre64
|dw:1443371398297:dw| oh good, choices, then we have something we can compare
amistre64
  • amistre64
what is our vertex of g, our biggest interval will then be along the y= axis of that vertex
anonymous
  • anonymous
-.5,3?
amistre64
  • amistre64
2|x+0.5| -3 ) -0.5, -3 is what it looks like to me, so when does f=-3?
anonymous
  • anonymous
Not sure
amistre64
  • amistre64
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 ...
anonymous
  • anonymous
Ok so what would that be?
amistre64
  • amistre64
im not going to do the algebra for you ...
anonymous
  • anonymous
xd ok bare with my laziness gimme a sec
anonymous
  • anonymous
x = -2 and x = 7?
amistre64
  • amistre64
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?
amistre64
  • amistre64
outside of -2 to 7, the min of f drops below the min of g .... g cant go lower than its vertex by default
anonymous
  • anonymous
I can rule D out
amistre64
  • amistre64
D is bad, and A goes to 8 so it is bad for us too
anonymous
  • anonymous
So is the answer none of these?
amistre64
  • amistre64
|dw:1443372355236:dw|
amistre64
  • amistre64
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?
anonymous
  • anonymous
So it's none of these?
amistre64
  • amistre64
you havent answered my question ...
anonymous
  • anonymous
All of them?
amistre64
  • amistre64
if your not understanding what I am asking for, then say so ...
anonymous
  • anonymous
Yeah what are you trying to ask?
amistre64
  • amistre64
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
anonymous
  • anonymous
|dw:1443372753726:dw|
amistre64
  • amistre64
now show me on that drawing, where 1 to 7 fits in ..
anonymous
  • anonymous
|dw:1443372851792:dw|
amistre64
  • amistre64
|dw:1443372874804:dw| is -0.5 in the interval from 1 to 7?
anonymous
  • anonymous
n0pe.
amistre64
  • amistre64
is -0.5 in the interval from -2 to 5?
anonymous
  • anonymous
yes
amistre64
  • amistre64
then we should pick that one.
anonymous
  • anonymous
So the answer is C?
amistre64
  • amistre64
i would go with C yes
anonymous
  • anonymous
Gracias!
amistre64
  • amistre64
de nada

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