Troubles with some math Translations

[Lorax]

Hey I'm having a few troubles with some Translations if anyone could help me out.


15. The graph of y=f(x). where f(x) = |x+4| + 1, its reflected in the y axis. This produces the same results as would translating the graph of y=f(x) to the right by how many units?

I was sick for a bit so I sort of forget or am unsure of how you'd figure that out. Essentially what does |x+4| + 1 look like? Is it a prabola or a straight line sort of deal. I think after that reminder I could manage.

Okay and here's a few more... They have pics so it might be hard... so I'll try and simplify.

if y=f(x^2) -3 what does y=1/f(x^2) -3 look like? Its multiple choice but its hard to explain since they are in picture format. What happens to parabola's when they are 1/f(x)?

Thanks

 

[HallsofIvy]

f(x)= |x+4| is a "bent" straight line. It is the straight line through (0,4) and (-4,0) to the right of x=-4 and then "bends" to go through (-5, 1) again.

f(x)= |x+4|+ 1 is that moved up 1.

Reflecting in the y-axis changes x to -x so (-4,1) to (4,1), same as translating 8 places to the right.