1. anonymous

2. anonymous

3. anonymous

this is what i get for graphing both, but the answers are confusing me.

4. idku

u don't need to graph the functions to determine the answer

5. anonymous

okay. how can i determine the answer without graphing them?

6. idku

$$\LARGE f(x)=2\log_{10}(x-1)-4$$ $$\LARGE g(x)=10(x-1)^2+4$$ first I just want to put the functions up not to click a different tab every time

7. anonymous

@mathstudent55

8. idku

the parent logarithmic function is $$\LARGE L(x)=\log_{10}(x)$$ (naming it L of x, becuase it is logarithmic) $$\LARGE L(x+a)=\log_{10}(x+a)$$ is a shift a units to the left $$\LARGE L(x+a)=\log_{10}(x-a)$$ is a shift a units to the right $$\LARGE L(x)=B\times \log_{10}(x)$$ multiples times a scale factor B

9. idku

how do you obtain the g(x) from a parent function $$\LARGE L(x)=\log_{10}(x)$$ ?

10. idku

i mean how do you obtain f(x) (not g of x)

11. mathstudent55

When you replace x with x - h, h being a number, the function is translated h units horizontally. When you replace y with y - k, k being a number, the function is translated k units vertically.

12. anonymous

so are you two saying that it's some sort of vertical shift?

13. anonymous

@mathstudent55

14. anonymous

@idku

15. anonymous

16. anonymous

@mathstudent55

17. anonymous

can someone help me?

18. anonymous

@mathstudent55

19. anonymous

@idku

20. anonymous

SOMEONE