State The Translation!

Question

1; g(x)=2f(x)+3

2: g(x)=1/2f(x+4)

3: g(x)=f(x-2)+5

4: g(x)=f(x)+1

5: g(x)=-4f(x)-8

6: g(x)=1/4f(x+2)-3

Answer 1

The translations are:

g(x) = a·f(x-b) + c

1. a = vertical dilation (stretch if |a|>1, shrink if |a|<1). Also flips the graph of f(x) across the x-axis if a<0)
2. b = horizontal shift (right is b>0, left if b<0)
3. c = vertical shift (up if c>0, down if c<0)

I'll do the first one:

g(x) = 2f(x) + 3

Here a = 2, b = 0, c = 3. Vertical stretch by a factor of 2, vertical shift up 3. You do the rest.