# 85+ CAT Functions and graphs questions With Video Solutions

CAT Functions, Graphs and Statistics questions are very important to practice while preparing for the CAT exam. Every year these questions frequently appear in the CAT question papers. Check out the below-given practice questions from this topic (functions, graphs and statistics). All these questions are taken from CAT's previous papers and separated year-wise.  Take free CAT mocks to understand the latest exam pattern and also you'll get a fair idea of how questions are asked. You can check out the important functions questions for CAT Quant. These are a good source for practice; If you want to practice these questions, you can download this CAT functions questions PDF below, which is completely Free.

## CAT Functions, Graphs and Statistics Questions Weightage Over Past 5 Years

 Year Weightage 2023 2 2022 5 2021 1 2020 8 2019 5 2018 3

## CAT Functions, Graphs and Statistics Formulas PDF

For individuals preparing for the CAT quant section formulas related to functions, graphs, and statistics, essential topics. This resource helps you to understand and mastering key concepts, providing a quick and efficient way to review and reinforce their knowledge in these areas. This PDF can be a helpful to understanding of CAT functions, graphs, and statistics formulas concepts relevant to the test.

Functions, Graphs and Statistics - Algebra Identities  Formulas:

$$(a+b)(a-b)$$ = $$\displaystyle (a^2-b^2)$$

$$(a^3-b^3)$$ = $$\displaystyle (a-b)(a^2+b^2+ab)$$

$$(a^3+b^3)$$ = $$\displaystyle (a+b)(a^2+b^2-ab)$$

$$(a+b+c)^2$$ = $$\displaystyle a^2+b^2+c^2+2(ab+bc+ca)$$

$$\displaystyle (a^3+b^3+c^3-3abc)$$ = $$\displaystyle (a+b+c) * (a^2+b^2+c^2 - ab - bc - ca)$$

If $$(a+b+c)=0$$ => $$\displaystyle a^3+b^3+c^3=3abc$$

$$(a+b)^2$$ = $$\displaystyle (a^2+b^2+2ab)$$

$$(a-b)^2$$ = $$\displaystyle (a^2+b^2-2ab)$$

$$(a+b)^3$$ = $$\displaystyle a^3+b^3+3ab(a+b)$$

$$(a-b)^3$$ = $$\displaystyle a^3-b^3-3ab(a-b)$$

One can practice these questions in a test format or can also download these questions in a PDF format along with the detailed video solutions for every question explained by the CAT toppers. Functions, Graphs and statistics is the one of the topic in CAT quant section, where the questions are mostly tricky. We have provided one solved set of questions on functions and graphs topic. Functions are one of the important topics in the Quantitative section of the CAT exam. It is an easy topic and so one must not avoid this topic. Every year 1-2 questions are asked on Functions. You can check out these Functions questions from CAT previous year papers. Practice a good number of questions on CAT Functions questions so that you don't miss out on the easy questions from this topic.

## CAT 2023 Functions, Graphs and Statistics questions

#### Question 1

The area of the quadrilateral bounded by the Y-axis, the line x = 5, and the lines $$\mid x-y\mid-\mid x-5\mid=2$$, is

#### Question 2

Suppose f(x, y) is a real-valued function such that f(3x + 2y, 2x - 5y) = 19x, for all real numbers x and y. The value of x for which f(x, 2x) = 27, is

## CAT 2022 Functions, Graphs and Statistics questions

#### Question 1

Let $$0 \leq a \leq x \leq 100$$ and $$f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\mid$$. Then the maximum value of f(x) becomes 100 when a is equal to

#### Question 2

Let $$f(x)$$ be a quadratic polynomial in $$x$$ such that $$f(x) \geq 0$$ for all real numbers $$x$$. If f(2) = 0 and f( 4) = 6, then f(-2) is equal to

#### Question 3

Suppose for all integers x, there are two functions f and g such that $$f(x) + f (x - 1) - 1 = 0$$ and $$g(x ) = x^{2}$$. If $$f\left(x^{2} - x \right) = 5$$, then the value of the sum f(g(5)) + g(f(5)) is

#### Question 4

Let r be a real number and $$f(x) = \begin{cases}2x -r & ifx \geq r\\ r &ifx < r\end{cases}$$. Then, the equation $$f(x) = f(f(x))$$ holds for all real values of $$x$$ where

#### Question 5

For any real number x, let [x] be the largest integer less than or equal to x. If $$\sum_{n=1}^N \left[\frac{1}{5} + \frac{n}{25}\right] = 25$$ then N is

## CAT 2021 Functions, Graphs and Statistics questions

#### Question 1

If $$f(x)=x^{2}-7x$$ and $$g(x)=x+3$$, then the minimum value of $$f(g(x))-3x$$ is:

## CAT 2020 Functions, Graphs and Statistics questions

#### Question 1

Let $$f(x)=x^{2}+ax+b$$ and $$g(x)=f(x+1)-f(x-1)$$. If $$f(x)\geq0$$ for all real x, and $$g(20)=72$$. then the smallest possible value of b is

#### Question 2

The number of real-valued solutions of the equation $$2^{x}+2^{-x}=2-(x-2)^{2}$$ is:

#### Question 3

The area of the region satisfying the inequalities $$\mid x\mid-y\leq1,y\geq0$$ and $$y\leq1$$ is

#### Question 4

In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by

#### Question 5

The area, in sq. units, enclosed by the lines $$x=2,y=\mid x-2\mid+4$$, the X-axis and the Y-axis is equal to

#### Question 6

If $$f(x+y)=f(x)f(y)$$ and $$f(5)=4$$, then $$f(10)-f(-10)$$ is equal to

#### Question 7

If $$f(5+x)=f(5-x)$$ for every real x, and $$f(x)=0$$ has four distinct real roots, then the sum of these roots is

#### Question 8

In how many ways can a pair of integers (x , a) be chosen such that $$x^{2}-2\mid x\mid+\mid a-2\mid=0$$ ?

## CAT 2019 Functions, Graphs and Statistics questions

#### Question 1

Consider a function f satisfying f (x + y) = f (x) f (y) where x,y are positive integers, and f(1) = 2. If f(a + 1) +f (a + 2) + ... + f(a + n) = 16 (2$$^n$$ - 1) then a is equal to

#### Question 2

For any positive integer n, let f(n) = n(n + 1) if n is even, and f(n) = n + 3 if n is odd. If m is a positive integer such that 8f(m + 1) - f(m) = 2, then m equals

#### Question 3

The number of the real roots of the equation $$2 \cos (x(x + 1)) = 2^x + 2^{-x}$$ is

#### Question 4

Let S be the set of all points (x, y) in the x-y plane such that $$\mid x \mid + \mid y \mid \leq 2$$ and $$\mid x \mid \geq 1.$$ Then, the area, in square units, of the region represented by S equals