Question

I need help for these! (if you could show the steps it'll help alot:) )

Answer 1

The attached picture is a summary of all the six transformations you'd do.

Any change outside the f(x) notation impacts y-values of points on the graph.

Any changes inside the f(x) notation impacts x-values of points on the graph.

The trick is that the inside changes are usually the opposite of what you'd expect to have happen.

7. y=f(x)+8

This is an outside change.  You're adding 8 to all the y-values of points on the graph.  This will shift your entire graph up 8 units.

8. y=f(x+6)

This is an inside change.  Because it says "+6", you want to think, "Ah!  That means I'll actually subtract 6 from the x-value of every point on the graph." This graph is shifted 6 units to the left.

9. y=-f(x)

Inside change, impacts y-values.  Every y-value will be given the opposite signs.  Negatives become positive and positives become negative.  This will flip your graph over the x-axis.

10. y = f(-x) + 5

Give this one a shot on your own first in a comment and I'll let you know how you did.  

11. y = - 3 f(x-3)

There are three things happening.  A negative on the outside, multiplying by 3 on the outside, and subtracting 3 inside.  What will each of those do individually?  Take a shot on this one and let me know what you think.

12. y = 1/2 f( 1/2 x )

Again, three changes.  Try this one and let me know what you think.  Remember multiplying by 1/2 inside really means you'll do the opposite of multiplying by 1/2.