KJ4UTS
  • KJ4UTS
Using graphs to determine the number of solutions x for each of the following equations. Please explain. Thank you!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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KJ4UTS
  • KJ4UTS
KJ4UTS
  • KJ4UTS
when they say f(x)=2 are they asking me to look on the x or y axis?
KJ4UTS
  • KJ4UTS

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More answers

Michele_Laino
  • Michele_Laino
you have to intersect the graph of \(f(x)\) with the line \(y=2\), then you have to search for the x-coordinates of the intersection points
KJ4UTS
  • KJ4UTS
do you know if the desmos calculator can plug in piecewise functions?
Michele_Laino
  • Michele_Laino
I don't know, sorry :(
KJ4UTS
  • KJ4UTS
so what you saying is a horizontal line at y=2 has to go across and what ever it hits thats the number?
KJ4UTS
  • KJ4UTS
I see two different lines on the graph so what if it hits both of the graphs
Michele_Laino
  • Michele_Laino
you can solve your exercise, using the first graph above, here is how: |dw:1446572358214:dw|
Michele_Laino
  • Michele_Laino
therefore, you have to do the same procedure using the subsequent lines: \(y=4,\;y=5,\;y=8\)
Michele_Laino
  • Michele_Laino
each time you have to search for the values of \(x_1,\;x_2\)
KJ4UTS
  • KJ4UTS
how do you search for x1 an y1 using the graph above
KJ4UTS
  • KJ4UTS
when you get those two values then what do you do?
Michele_Laino
  • Michele_Laino
you have to use the millimeter paper
KJ4UTS
  • KJ4UTS
then what do you do with the two values doesn't the answer have to be one value
Michele_Laino
  • Michele_Laino
for example, using desmos, I got this graph:
1 Attachment
Michele_Laino
  • Michele_Laino
now, x=1.085 is less than 2, so x=1.085 is a solution, furthermore, x=3 is greater than 2, so x=3 is the other solution FInally, if we have no intersections, then our equation has no solutions If I use the line \(y=8\) you should get no solutions, please check
KJ4UTS
  • KJ4UTS
ok let me check
KJ4UTS
  • KJ4UTS
1 Attachment
KJ4UTS
  • KJ4UTS
yeah it says 0
Michele_Laino
  • Michele_Laino
ok! :)
KJ4UTS
  • KJ4UTS
so I use the one on the left
KJ4UTS
  • KJ4UTS
oh so for f(x)=2 there is 2 solutions
Michele_Laino
  • Michele_Laino
correct! If \(f(x)=2\) we have 2 solutions, if \(f(x)=8\) we have no solutions
KJ4UTS
  • KJ4UTS
this is what I got for 4
1 Attachment
Michele_Laino
  • Michele_Laino
\(f(x)=8\) gives no solutions, since x=2.169 >2, and x=0.8 < 2
Michele_Laino
  • Michele_Laino
correct! we have 2 solutions
Michele_Laino
  • Michele_Laino
for \(f(x)=4\)
KJ4UTS
  • KJ4UTS
so f(x)=4 it is 2 solutions also
KJ4UTS
  • KJ4UTS
1 Attachment
KJ4UTS
  • KJ4UTS
so does that mean f(x)=5 has two solutions also?
Michele_Laino
  • Michele_Laino
here: \(f(x)=5\) gives one solution, since x=1.5, is less than 2
Michele_Laino
  • Michele_Laino
the intersection with the blue lines, are acceptable, if the corresponding x-coordinate is greater or equal to 2, please refer to your definition of the piecewise function
Michele_Laino
  • Michele_Laino
line*
KJ4UTS
  • KJ4UTS
I see so for these problems we also have to use the: 0 <= x < 2 2 <= x <= 4 along with the graph
Michele_Laino
  • Michele_Laino
correct!
KJ4UTS
  • KJ4UTS
so f(x)=2 has 2 solutions f(x)=4 has 2 solutions f(x)=5 has 1 solution f(x)=8 has 0 solutions I understand this better now I will study everything we talked about thank you for taking the time to explain this to me :)
Michele_Laino
  • Michele_Laino
:)

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