1.
[tex]f(x)=2x+3\\\\I.g(x)=2(x-1)+3=2x-2+3=2x+1\\g(x)=2x+2\\\\II.h(x)=2x+3+4=2x+7\\h(x)=2x+7\\\\III.i(x)=-(2x+3)=-2x-3\\i(x)=-2x-3\\\\IV.k(x)=2(-x)+3=-2x+3\\k(x)=-2x+3\\\\V.f(x)=|2x+3|[/tex]
2.
[tex]f(x)=\sqrt{x}\\\\I.g(x)=\sqrt{x-1}\\\\II.h(x)=\sqrt{x}+4\\\\III.i(x)=-\sqrt{x}\\\\IV.k(x)=\sqrt{-x}\\\\V. f(x)=|\sqrt{x}|=\sqrt{x}\\f(x)=\sqrt{x}[/tex]
3.
[tex]f(x)=|x-1|+3\\\\I.g(x)=|x-1-1|+3\\g(x)=|x-2|+3\\\\II.h(x)=|x-1|+3+4=|x-1|+7\\h(x)=|x-1|+7\\\\III. i(x)=-(|x-1|+3)=-|x-1|-3\\i(x)=-|x-1|-3\\\\IV.k(x)=|-x-1|+3\\\\V. f(x)=||x-1|+3|=|x-1|+3\\f(x)=|x-1|+3[/tex]
4.
[tex]f(x)=|x|+x\\\\I.g(x)=|x-1|+x-1\\\\II.h(x)=|x|+x+4\\\\III.i(x)=-(|x|+x)=-|x|-x\\i(x)=-|x|-x\\\\IV.k(x)=|-x|-x=|x|+x\\k(x)=|x|+x\\\\V.f(x)=||x|+x|=|x|+x\\f(x)=|x|+x[/tex]
5.
[tex]f(x)=\sqrt{x-8}\\\\I.g(x)=\sqrt{x-1-8}=\sqrt{x-9}\\g(x)=\sqrt{x-9}\\\\II.h(x)=\sqrt{x-8}+4\\\\III.i(x)=-\sqrt{x-8}\\\\IV.k(x)=\sqrt{-x-8}\\\\V.f(x)=|\sqrt{x-8}|=\sqrt{x-8}\\f(x)=\sqrt{x-8}[/tex]
6.
[tex]f(x)=\sqrt{x+1}-6\\I.g(x)=\sqrt{x-1+1}-6=\sqrt{x}-6\\g(x)=\sqrt{x}-6\\\\II.h(x)=\sqrt{x+1}-6+4=\sqrt{x+1}-2\\\\III.i(x)=-(\sqrt{x+1}-6)=-\sqrt{x+1}+6\\i(x)=-\sqrt{x+1}+6\\\\IV.k(x)=\sqrt{-x+1}-6\\\\V.f(x)=|\sqrt{x+1}-6|[/tex]
7.
[tex]f(x)=x^2+2x-6\\\\I.g(x)=(x-1)^2+2(x-1)-6=x^2-2x+1+2x-2-6=x^2-7\\g(x)=x^2-7\\\\II.h(x)=x^2+2x-6+4=x^2+2x-2\\h(x)=x^2+2x-2\\\\III.i(x)=-(x^2+2x-6)=-x^2-2x+6\\i(x)=-x^2-2x+6\\\\IV.k(x)=(-x)^2+2(-x)-6=x^2-2x-6\\k(x)=x^2-2x-6\\\\V.f(x)=|x^2+2x-6|[/tex]
8.
[tex]f(x)=2x^2+3\\\\I.g(x)=2(x-1)^2+3=2x^2-4x+2+3=2x^2-4x+5\\g(x)=2x^2-4x+5\\\\II.h(x)=2x^2+3+4=2x^2+7\\h(x)=2x^2+7\\\\III.i(x)=-(2x^2+3)=-2x^2-3\\i(x)=-2x^2-3\\\\IV.k(x)=2(-x)^2+3=2x^2+3\\k(x)=2x^2+3\\\\V.f(x)=|2x^2+3|=2x^2+3\\f(x)=2x^2+3[/tex]
9.
[tex]f(x)=\frac{1}{x}\\\\I.g(x)=\frac{1}{x-1}\\\\II.~~h(x)=\frac{1}{x}+4=\frac{1}{x}+\frac{4x}{x}=\frac{4x+1}{x}\\h(x)=\frac{4x+1}{x}\\\\III.i(x)=-\frac{1}{x}\\\\IV.k(x)=\frac{1}{-x}=-\frac{1}{x}\\k(x)=-\frac{1}{x}\\\\V.f(x)=|\frac{1}{x}|[/tex]
10.
[tex]f(x)=\frac{x+2}{x-6}\\\\I.g(x)=\frac{x-1+2}{x-1-6}=\frac{x+1}{x-7}\\g(x)=\frac{x+1}{x-7}\\\\II.h(x)=\frac{x+2}{x-6}+4=\frac{x+2}{x-6}+\frac{4x-24}{x-6}=\frac{5x-22}{x-6}\\h(x)=\frac{5x-22}{x-6}\\\\III.i(x)=-\frac{x+2}{x-6}\\\\IV.k(x)=\frac{-x+2}{-x-6}=\frac{-(x-2)}{-(x+6)}=\frac{x-2}{x+6}\\k(x)=\frac{x-2}{x+6}\\\\V.f(x)=|\frac{x+2}{x-6}|[/tex]
11.
[tex]f(x)=\frac{x-5}{x}\\\\I.g(x)=\frac{x-1-5}{x-1}=\frac{x-6}{x-1}\\g(x)=\frac{x-6}{x-1}\\\\II. h(x)=\frac{x-5}{x}+4=\frac{x-5}{x}+\frac{4x}{x}=\frac{5x-5}{x}\\h(x)=\frac{5x-5}{x}\\\\III.i(x)=-\frac{x-5}{x}\\\\IV. k(x)=\frac{-x-5}{-x}=\frac{-(x+5)}{-x}=\frac{x+5}{x}\\k(x)=\frac{x+5}{x}\\\\V.f(x)=|\frac{x-5}{x}|[/tex]
Z góry przepraszam za błędy (jeśli takowe wystąpią), mam nadzieję że pomogłem
