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.

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Year | Weightage |

2023 | 2 |

2022 | 5 |

2021 | 1 |

2020 | 8 |

2019 | 5 |

2018 | 3 |

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.

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

correct answer:-**45**

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

correct answer:-**3**

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

correct answer:-**3**

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

correct answer:-**2**

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

correct answer:-**12**

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

correct answer:-**2**

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

correct answer:-**44**

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

correct answer:-**4**

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

correct answer:-**2**

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

correct answer:-**4**

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

correct answer:-**3**

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

correct answer:-**2**

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

correct answer:-**1**

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

correct answer:-**3**

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

correct answer:-**4**

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

correct answer:-**4**

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

correct answer:-**3**

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

correct answer:-**10**

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

correct answer:-**2**

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

correct answer:-**2**

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