## Thomas' Calculus 13th Edition

a. $g(x-3)+\frac{1}{2}$ b. $g(x+\frac{2}{3})-2$ c. $g(-x)$ d. $-g(x)$ e. $5g(x)$ f. $g(5x)$
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 $y-axis$