Question

Question in screenshot

Answer 1

Im pretty sure D but makin sure

Answer 2

Here's a summary of translations of function f(x) (parent function) into the image (new function) g(x).

1. Horizontal translation, to the right by h units:
g(x)=f(x-h)........................h is positive
2. Horizontal translation, to the left, by h units.
Same as 1, but h is negative
g(x)=f(x-h)........................h is negative (left)

3. Vertical translation, up by k units.
g(x)=f(x)+k..............k is positive
4. Vertical translation, down by k units.
Same as 3. But k is negative
g(x)=f(x)+k..............k is negative (down)

In summary, to translate (shift) the parent function to the right by h units and up by k units, we do
g(x)=f(x-h)+k
Adjust the signs of h and k for different directions.

For example, to shift the parent function \(f(x)=1/x^2\) 5 units to the LEFT and 3 units UP, we use h=-5, k=+3 to arrive at:
\(g(x)=\frac{1}{(x-(-5))^2} + 3\), or on simplification
\(g(x)=\frac{1}{(x+5)^2} + 3\)

By applying the above, you will be able to figure the correct response.

Answer 3

D is actually moving the graph F(x) = 1/x up 4 units.

Adding a constant outside the function will be moving the function up or down i.e. f(x) + k for k units up or f(x) - k for k units down.
To move left or right we must evaluate f(x-R) for R units right or f(x+L) for L units left.

Mathmate has given some nice transformations to look at.