2 the modulus of a linear function

Question 1

What should be done when a graph is f(|x|) (mod is inside the x.

Answer 1

Everything on the right side should be reflected on the left side as all the x coordinates will have the same output that they have on the right hand side.

Question 2

What should be done when a graph is |f(x)| mod is on the outside of f(x).

Answer 2

Everything under the x axis gets reflected above the x axis. As the y coordinates can only be positive.

Question 3

Why will f^-1 not exist?

Answer 3

As f(x) is a many to one function and the inverse would
be a one to many function which cannot exist.

Question 4

How do you solve mod equations?

Answer 4

Step 1-Square both sides and solve

Step 2 Sketch the graphs to ensure no points have been missed.

Question 5

How do you know when a linear function will have no solutions with a mod function?

Answer 5

-Ensure the linear functions is above or below the turning point of the mod function.

Question 6

how would you translate 2-2/3|x+1|

Answer 6

Draw |x+1| and multiply y coordinates by -2/3 and add them by 2