#### Answer

(a) shift $f(x)$ left 5 units, stretch vertically by a factor of 2, and shift down 1 unit
(b) shift $f(x)$ right 3 units, shrink vertically by a factor of $\frac{1}{4}$ and shift up 5 units

#### Work Step by Step

(a) We can obtain $2f(x+5)-1$ by shifting $f(x)$ left 5 units, stretching the graph vertically by a factor of 2 and shifting the graph down 1 unit.
(b) We can obtain $\frac{1}{4}f(x-3)+5$ by shifting $f(x)$ right 3 units, shrinking the graph vertically by a factor of $\frac{1}{4}$ and shifting the graph up 5 units.