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# C1 graph question watch

1. Hi just wondering why does a ii) only have one solution? I thought both lines meet at 2,0 and -2,0... thanks.
2. Draw the line y = -x on the graph, you should see that they only cross once.
3. (Original post by coconut64)
Hi just wondering why does a ii) only have one solution? I thought both lines meet at 2,0 and -2,0... thanks.
It will only meet the graph once.

Draw the line y=-x and you'll see it'll intersect only once; if you're struggling to visualise it, a table of values is always the best thing to do
4. This is a question from Solomon Papers, I think.
5. (Original post by coconut64)
Hi just wondering why does a ii) only have one solution? I thought both lines meet at 2,0 and -2,0... thanks.
Look at the gradient of the f(x) graph in the negative region, it goes from -2 to 0 in the x-direction and that makes it go from 0 to 2 in the y-direction, so it has a gradient of .

That's the same gradient as the line y=-x. so if you plot y=-x, it will always be two units behind (x-direction) wise f(x) in the negative region since they have the same gradient and hence increase/decrease at the same rate, but their 'starting point' is different.

Edit to add: in a more formal manner, you can define piecewise such that it is for , then in the left-half plane, it will intersect if and only if . Which is false. So it won't intersect in the left-half plane.

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Updated: February 25, 2016
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