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Sketching with a modulus core 3

If I’m asked to sketch y=2|x+4k| where k is a constant, how would I do it?
I know I would set y=0 but when I do this I get
2x+8k=0 and then x= -4K is this right? or would the modulus sign mean I change it to x=4K? Sorry if this sounds stupid.
Original post by imundercover
If I’m asked to sketch y=2|x+4k| where k is a constant, how would I do it?
I know I would set y=0 but when I do this I get
2x+8k=0 and then x= -4K is this right? or would the modulus sign mean I change it to x=4K? Sorry if this sounds stupid.


You can just work up in stages by considering transformations.

1) Start with y=xy=x

2) How would y=∣x∣y=|x| look like?

3) How does the last one transform to give y=2∣x∣y=2|x| ?

4) How does the last one transform to give y=2∣x+4k∣y=2|x+4k| ?
Original post by RDKGames
You can just work up in stages by considering transformations.

1) Start with y=xy=x

2) How would y=∣x∣y=|x| look like?

3) How does the last one transform to give y=2∣x∣y=2|x| ?

4) How does the last one transform to give y=2∣x+4k∣y=2|x+4k| ?


Thank you! I did this and it helped so much! So can you just confirm the x intercept is -4K because I think it is?
Original post by imundercover
Thank you! I did this and it helped so much! So can you just confirm the x intercept is -4K because I think it is?


Yes the x-intercept is x=−4kx=-4k

You can also do it in a different way by first finding this intercept, then sketching the function y=−2(x+4k)y=-2(x+4k) for the region x<4kx<4k, and sketching the function y=2(x+4k)y=2(x+4k) for the region x≥4kx \geq 4k

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