## Thomas' Calculus 13th Edition

a. shift $f(x)$ to the right 5 units. b. compress horizontally by a factor of 4. c. reflect about the y-axis and compress horizontally by a factor of 3. d. compress horizontally by a factor of 2 and shift left 1/2 unit. e. Stretch horizontally by a factor of 3 and shift down 4 units. f. Reflect around x-axis, stretch vertically by a factor of 3, and shift up 1/4 unit.
Recall the general rules for graph transformations (here $a,b,c,d$ are integers): $(x+c)\implies$ shift left by $c$ $(x-c)\implies$ shift right by $c$ $f(x)+d\implies$ shift up by $d$ $f(x)-d\implies$ shift down by $d$ $af(x)$ stretch graph by $a$ vertically $\dfrac{1}{a}f(x)$ shrink graph by $a$ vertically $f(bx)$ shrink graph by $b$ horizontally $f(\dfrac{x}{b})$ stretch graph by $b$ horizontally $-f(x)$ reflect around $x-axis$ $f(-x)$ reflect around $y-axis$