Question

Using graphs to determine the number of solutions x for each of the following equations.

Please explain. Thank you!

Answer 1

when they say f(x)=2 are they asking me to look on the x or y axis?

Answer 2

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

Answer 3

do you know if the desmos calculator can plug in piecewise functions?

Answer 4

I don't know, sorry :(

Answer 5

so what you saying is a horizontal line at y=2 has to go across and what ever it hits thats the number?

Answer 6

I see two different lines on the graph so what if it hits both of the graphs

Answer 7

you can solve your exercise, using the first graph above, here is how:

Answer 8

therefore, you have to do the same procedure using the subsequent lines:
\(y=4,\;y=5,\;y=8\)

Answer 9

each time you have to search for the values of \(x_1,\;x_2\)

Answer 10

how do you search for x1 an y1 using the graph above

Answer 11

when you get those two values then what do you do?

Answer 12

you have to use the millimeter paper

Answer 13

then what do you do with the two values doesn't the answer have to be one value

Answer 14

for example, using desmos, I got this graph:

Answer 15

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

Answer 16

ok let me check

Answer 17

yeah it says 0

Answer 18

ok! :)

Answer 19

so I use the one on the left

Answer 20

oh so for f(x)=2 there is 2 solutions

Answer 21

correct! If \(f(x)=2\) we have 2 solutions, if \(f(x)=8\) we have no solutions

Answer 22

this is what I got for 4

Answer 23

\(f(x)=8\) gives no solutions, since x=2.169 >2, and x=0.8 < 2

Answer 24

correct! we have 2 solutions

Answer 25

for \(f(x)=4\)

Answer 26

so f(x)=4 it is 2 solutions also

Answer 27

so does that mean f(x)=5 has two solutions also?

Answer 28

here: \(f(x)=5\) gives one solution, since x=1.5, is less than 2

Answer 29

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

Answer 30

line*