Staceyy 3 years ago how do you graph this function?please show work! g(x)=5|x-4|+2

1. Walleye

There could be a little trick to this but I havent done one like this in a loong time. Start with g(x) = abs(x) You know what that graph looks like Then make the transformation to g(x) = abs(x - 4) and keep going until you got your whole function

2. across

That's the best way to do it, imho.

3. Staceyy

I'm sorry, can you explain it a little more thoroughly Walleye?

4. across

Do you know what the graph of\[f(x)=|x|\]looks like?

5. Staceyy

yes i do

6. across

What would happen to that graph if we do this\[f(x)=|x-4|\]

7. Staceyy

it would move over 4 to the right, right?

8. Walleye

Thanks Across, you seem to be very good in math :D

9. across

That's correct! Now, what would happen to it if we multiply it by five like this\[f(x)=5|x-4|\]

10. across

Aww thank you Walleye :)

11. Staceyy

I'm not really sure :( sry. i know that the graph is going to move up 2 tho, right?

12. across

It is almost the same thing as multiplying\[f(x)=x\]by 5\[f(x)=5x.\]The slope of the line gets "steeper." :)

13. Walleye

If i may, think of the function f(x) = x and f(x) = 5x What happens when you mutiply f(x) = x by 5??

14. Walleye

Copycat!

15. Staceyy

so then it does down 5?

16. Staceyy

*goes

17. across

No, the graph gets "steeper" like this (see attached).

18. across

Finally, I'm sure you already knows what will happen to the graph if we add two to it\[f(x)=5|x-4|+2\]

19. across

know*

20. Walleye

Try graphing all of these functions yourself and you will get a feel for how these transformations affect the function

21. Staceyy

I got it! Thank you guys so much :) I appreciate it!

22. Walleye

No problem!!! Practicing problems like these can be a bore but soon enough you will get good enough to see most any function and know what it looks like right away!!

23. Staceyy

Lol! it's true, they are a bore :) thanks again!

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