Class 9th math 3.3 solution english PCTB

Note: This is the Solution of review exercise 3.3 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.

Exercise 3.3

Question # 01: For \(\small{A=\{1,2,3,4\}}\), find the following relations in \(\small{A}\). State the domain and range of each relation.

\((i)\) \(\quad\) \(\{ (x,y)|y=x\} \)

\((ii)\) \(\quad\) \(\{ (x,y)|y+x=5\} \)

\((iii)\) \(\quad\) \(\{ (x,y)|x+y<5\} \)

\((iv)\) \(\quad\) \(\{ (x,y)|x+y>5\} \)

Question 2: Which of the following diagrams represent functions and of which type?

Question 3: If \(\small{g(x)=3x+2}\) and \(\small{h(x)=x^2+1}\), then find:

\((i)\) \(\quad\) \(g(0) \)

\((ii)\) \(\quad\) \(g(-3)\)

\((iii)\) \(\quad\) \(g(\frac{2}{3}) \)

\((iv)\) \(\quad \)\(h(1)\)

\((v)\) \(\quad \) \(h(-4) \)

\((vi)\) \(\quad \) \(h(-\frac{1}{2})\)

Question 4: Given that \(\small{f(x)=ax+b+1}\), where \(\small{a}\) and \(\small{b}\) are constant numbers. If \(\small{f(3)=8}\) and \(\small{f(6)=14}\), then find the values of \(\small{a}\) and \(\small{b}\).

Question 5: Given that \(\small{g(x)=ax+b+5}\), where \(\small{a}\) and \(\small{b}\) are constant numbers. If \(\small{g(-1)=0}\) and \(\small{g(2)=10}\), find the values of \(\small{a}\) and \(\small{b}\).

Question 6: Consider the function defined by \(\small{f(x)=5x+1}\). If \(\small{f(x)=32}\), find the \(\small{x}\) value.

Question 7: Consider the function defined by \(\small{f(x)=cx^2+d}\), where \(\small{c}\) and \(\small{d}\) are constant numbers. If \(\small{f(1)=6}\) and \(\small{f(-2)=10}\), then find the values of \(\small{c}\) and \(\small{d}\).