Transformation ? s? of? (??x) ? 2 Use shifts and scalings to transform the gra? p? of f??? ) ?= x2 into the grap ? h of ? . Use a graphing utility only to check your work. ? ? a.?? (?x)? f(x ? 3) ? ? ? ? b.? ? ) ?= f(2? ? 4) ? ? ? ? c ?g(?x)= ?3f? (?x ? 2) + 4 d.?

Step-by-step solution Step 1 of 9 We have to replace the value of x by x-3 in the function x , like follows: 2 2 2 Developing the expression , using the formula (a b) = a 2ab + b : Step 2 of 9 Remember these tips when we shift functions horizontally and vertically: horizontally k units to the right : (x-k) horizontally k units to the left : (x+k) vertically h units upwards : (x)+ h vertically h units downwards : (x)- h Step 3 of 9 Step 4 of 9 Step 5 of 9 Applying distributive property and grouping, we have: