Using the graph at right of $f(x)$, sketch the following functions (draw each on a separate grid).

1. $f(x) + 2$

   Hint (a):

   The function value, $f(x)$, is the $y$-value. How does the graph change if $2$ is added to each $y$-value?

2. $2f(x + 1)$

   Hint (b):

   New function: If $x = 1$, $f$(new) is equivalent to $f(2)$ from the original function. Also, what does multiplication by $2$ do to the function?

3. $−f(x - 2)$

   Hint (c):

   See part (b). Also, $f(x)$ became $−f(x)$, or $y$ became $−y$.

4. $f(2x)$

   Hint (d):

   $f(8)$ in the original function occurs
   when $x = 4$ in the new function.