Explore Exams
Login Signup
Sign in Open App
All Exams  >   Grade 8  >   Mathematics for Grade 8  >   All Questions

All questions of Functions for Grade 8 Exam

If f(x) = x2 and g(x) = cosx, which of the following is true?
  • a)
    f + g is even function
  • b)
    f – g is an odd function
  • c)
    f + g is not defined
  • d)
    f + g is an odd function
Correct answer is option 'A'. Can you explain this answer?

Raghav Bansal answered
if f(x) is an odd function
So, f(−x)=−f(x)
F(−x)=cos(f(−x))
=cos(−f(x))
=cos(f(x))
=F(x)
So cos(f(x)) is an even function
So, f(x) and g(x) is an even function
Clear all your doubts with EduRev

If A = {1, 2, 3}, and B = {3, 6} then the number of relations from A to B is
  • a)
    32
  • b)
    23
  • c)
    23
  • d)
    26
Correct answer is option 'D'. Can you explain this answer?

Preeti Iyer answered
The number of relations between sets can be calculated using 2mn where m and n represent the number of members in each set.
So, number of relations from A to B is 26.

Let R be a relation defined as
R = {(x, y): y = 2x, x is natural number < 5} then Range of R is given as ,
  • a)
    {2, 4, 6, 8}
  • b)
    {2, 4, 6, 8, 10}
  • c)
    {1, 2, 3, 4}
  • d)
    N
Correct answer is option 'A'. Can you explain this answer?

Gaurav Kumar answered
X is a natural number and x < 5, the number is 1, 2, 3, 4
y = 2x
► x(1), y = 2 × 1 = 2
► x(2), y = 2 × 2 = 4
► x(3), y = 2 × 3 = 6
► x(4), y = 2 × 4 = 8
Range = {2, 4, 6, 8}

Which of the following is not an example of polynomial function ?
  • a)
    g(x) = 8x2 + 5x – 2
  • b)
    p(x) =5x3 + 3x2 + x – 2
  • c)
    h(x) =3 root of x minus 1 over x
  • d)
    f(x) = 3x2 + x – 2
Correct answer is option 'C'. Can you explain this answer?

Lavanya Menon answered
A polynomial function is a function which involves only non-negative integer powers or only positive integer exponents of a variable in an equation.
In option C, powers of x are negative and fractional.

 If X = {1, 2, 3, 4}, Y = {1, 2, 3,…., 20}, and f: X –> Y be the correspondence which assigns each element in X the value equal to its square, then the domain, co-domain and range of f is
  • a)
    Domain = {1, 2, …, 20}, Range = {1, 2, 3, 4}, Co domain = {1, 2, 3, 4}
  • b)
    Domain = {1, 4, 9, 16}, Range = {1, 2, 3, 4}, Co domain = {1, 2, 3, …, 16}
  • c)
    Domain = {1, 2, 3, 4}, Range = {1, 4, 9, 16}, Co domain = {1, 2, 3, …, 20}
  • d)
    Domain = {1, 2, 3, 4}, Range = {1, 4, 9, 16}, Co domain = {1, 2, 3, …, 16}
Correct answer is option 'B'. Can you explain this answer?

Raghav Bansal answered
The correct option is B
Since the function is defined from 
XY.So the domain will be the set X which is {1,2,3,4}. Codomain is  what may possibly come out of a function. So codomain is the whole set Y which is {1,2,3,...,20}. Range is The range is the set of possible output values which will be the values in the set of Y which have a pre-image. That is, the value of squares. So the range is {1,4,,9,16}. 

Which of the following relations is not a function?
  • a)
    R= {(1,2), (3,4),(2,1),(5,1)}
  • b)
    R={(1,2), (1,4)(3,1),(5,1)}
  • c)
    R= {(1,2), (3,4)(2,1),(5,2)}
  • d)
    R= {(2,1), (4,4)(3,1),(5,1)}
Correct answer is option 'B'. Can you explain this answer?

Gaurav Kumar answered
A function is a relation in which no two ordered pairs have the same first element. A function associates each element in its domain with one and only one element in its range. R={(1,2), (1,4)(3,1),(5,1)} is not  a function because all the first elements are not different.

The function f : R → R defined by y = f(x) = 5 for each x ∈ R is
  • a)
    Modulus function
  • b)
    Signum function
  • c)
    Identity function
  • d)
    Constant function
Correct answer is option 'D'. Can you explain this answer?

Pioneer Academy answered
Constant Function is defined as the real valued function.
f: R→R, y = f(x) = c for each x∈R and c is a constant.
So ,this function basically associate each real number to a constant value.
It is a linear function where f(x1) = f(x2) for all x1,x2 ∈R

Which of the following is incorrect?
  • a)
    Modulus function, Domain: R; Range: [0, infinity)
  • b)
    Signum function, Domain: R; Range: {-1, 0,1}
  • c)
    Constant function, Domain: R; Range: R
  • d)
    Identity function, Domain: R; Range: R
Correct answer is option 'C'. Can you explain this answer?

Preeti Khanna answered
Constant Function is defined as the real valued function.
f : R→R, y = f(x) = c for each x∈R and c is a constant.
So, this function basically associate each real number to a constant value.
It is a linear function where f(x1) = f(x2) for all x1,x2 ∈ R
For f : R→R, y = f(x) = c for each x ∈ R
Domain = R
Range = {c}
The value of c can be any real number.

Number of subsets of a set of order three is
  • a)
    2
  • b)
    4
  • c)
    6
  • d)
    8
Correct answer is option 'D'. Can you explain this answer?

Raj Ghoshal answered
Number of Subsets of a Set of Order Three

To find the number of subsets of a set of order three, we need to consider all possible combinations of elements in the set.

Let's say we have a set S = {a, b, c}. We can represent each element of the set as a binary digit, where 0 represents the absence of the element and 1 represents the presence of the element.

- Empty Set: The empty set is a subset of every set, so it is included.
- Single Element Subsets: There are three single element subsets - {a}, {b}, and {c}.
- Two Element Subsets: There are three possible two-element subsets - {a, b}, {a, c}, and {b, c}.
- Three Element Subset: There is only one three-element subset - {a, b, c}.

Therefore, the total number of subsets of the set S = {a, b, c} is 1 (empty set) + 3 (single element subsets) + 3 (two-element subsets) + 1 (three-element subset) = 8.

Hence, the correct answer is option 'D' - 8.

In summary, to find the number of subsets of a set of order three, we consider all possible combinations of elements, including the empty set and subsets of different sizes. By applying this approach to the given set S = {a, b, c}, we find that there are 8 subsets in total.

The domain of the function f(x)=   is all real x such that
  • a)
    x<2
  • b)
    -2
  • c)
    -2 ≤ x ≤ 2
  • d)
    x>-2
Correct answer is option 'C'. Can you explain this answer?

Geetika Shah answered
4 - x2 = 0
=> (2+x)(2-x) = 0
x = +-2
Now select a test point, let it be x = 0. Then y = (4 - (0)2)1/2 = 2, so the function is defined on [-2,2]
Thus, the graph of y = (4 - x2)1/2 is a semicircle with radius 2 and domain is [-2,2]

f(x) = x is called
  • a)
    an identity function
  • b)
    a constant function
  • c)
    inverse function
  • d)
    step function
Correct answer is option 'A'. Can you explain this answer?

Mira Sharma answered
In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. In equations, the function is given by f(x) = x.

 Which of the following is not true for a parallelogram?    
  • a)
    Diagonals bisect each other
  • b)
    Opposite sides are equal
  • c)
    Opposite angles are equal
  • d)
    Opposite angles are bisected by the diagonals
Correct answer is option 'D'. Can you explain this answer?

Imk Pathshala answered
The statement that opposite angles are bisected by the diagonals is not generally true. This property does not hold for every parallelogram; it only occurs in special cases such as a rectangle or a rhombus under certain conditions.
Thus, the option that is not always true for a parallelogram is:
Option D:  Opposite angles are bisected by the diagonals.

Which of the following is not true?
  • a)
    Every relation from the set A to the set B is a function from the set A to the set B.
  • b)
    If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where a is called the pre-image of b under f.
  • c)
    Every function from the set A to the set B is a relation from the set A to the set B
  • d)
    If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where b is called the image of a under f.
Correct answer is option 'A'. Can you explain this answer?

Pooja Shah answered
A relation f from a set A to a set B is said to be function if every element of set A has one and only one image in set B. In other words, a function f is a relation such that no two pairs in the relation has the same first element. The notation f : X →Y means that f is a function from X to Y.

 If f(x) = x2 – x + 1; g(x) = 7x – 3, be two real functions then (f + g)(3) is
  • a)
    25
  • b)
    3
  • c)
    7
  • d)
    18
Correct answer is option 'A'. Can you explain this answer?

Riya Banerjee answered
 f(x) = x2 – x + 1; g(x) = 7x – 3
(f+g)(x) = (x2 - x + 1 + 7x - 3)
=(x2 - x + 7x + 1 - 3)
= x2 + 6x - 2
(f+g)(3) = x2 + 6x - 2
= (3)2 + 6(3) - 2
= 9 + 18 - 2
= 25

Find the domain of the function f(x) = 
  • a)
    R – {-4}
  • b)
    R
  • c)
    R – {4}
  • d)
    R+
Correct answer is option 'C'. Can you explain this answer?

Lavanya Menon answered
 f(x) = 3x/2x-8
denominator can't be zero so
2x - 8 not equal to 0
x should not equal to 4
we have domain R - {4}

Find the domain and range of the relation R given by:
R = {(x, y) : y = x + 6 / x, where x, y ∈ N and x < 6}
  • a)
    Domain of R = {1, 2, 3}
    Range of R = {7, 5}
  • b)
    Domain of R = {1, 2}
    Range of R = {7, 5}
  • c)
    Domain of R = {4, 5, 6}
    Range of R = {7, 3}
  • d)
    Domain of R = {2, 3}
    Range of R = {6, 5}
Correct answer is option 'A'. Can you explain this answer?

Nipun Tuteja answered
When x = 1:
y = 1 + 6 / 1
y = 1 + 6 = 7
So (1, 7) ∈ R.
Again for x = 2:
y = 2 + 6 / 2
y = 2 + 3 = 5
So (2, 5) ∈ R.
Again for x = 3:
y = 3 + 6 / 3
y = 3 + 2 = 5
So (3, 5) ∈ R.
Similarly for x = 4:
For x = 4:
y = 4 + 6 / 4
y = 4 + 1.5, but this is not a natural number (∉ N).
For x = 5:
y = 5 + 6 / 5
y = 5 + 1.2, but this is also not a natural number (∉ N).
Thus, the relation R = {(1, 7), (2, 5), (3, 5)}.
Where:
Domain of R = {1, 2, 3}
Range of R = {7, 5}

Which of the relations is not a function?
  • a)
    one many
  • b)
    domain = codomain
  • c)
    many one
  • d)
    one-one
Correct answer is option 'A'. Can you explain this answer?

Rohan Singh answered
One-to-one and many-to-one functions. A function is said to be one-to-one if every y value has exactly one x value mapped onto it, and many-to-one if there are y values that have more than one x value mapped onto them. This graph shows a many-to-one function.

If n(A) = 2, n(B) = 2. What is the total number of relations from A to B?
  • a)
    4
  • b)
    32
  • c)
    12
  • d)
    16
Correct answer is option 'D'. Can you explain this answer?

Varun Kapoor answered
Hint: To solve this problem you don’t need to count the number of relations by assuming it on your own. Use the formula of the number of relations from set A to set B. 

Complete step-by-step answer:
 It is given that A = {1, 2} and B = {3, 4}
The number of elements in A is n(A)=2 and that of B is n(B) = 2.
The formula for the number of relations from one set to another is:
⇒2(number of elements in the first set) x (number of elements of the second set) 
Therefore, we can write it as follows.
No. of relations from set A to set B = 2n(A)n(B) =  2(2*2) = 16 
Hence, the number of relations from A to B is 16.

ABCD is a parallelogram in which the bisectors of angles ∠A and ∠B intersect at point P then ∠APB is
  • a)
    45°
  • b)
    90°
  • c)
    60°
  • d)
    80°
Correct answer is option 'B'. Can you explain this answer?

Imk Pathshala answered
Since ABCD is a Parallelogram. Therefore,
AD || BC
AB is a transversal . Therefore ,

A + B = 180°. [ Consecutive interior angles]

Multiply both sides by 1/2 ,

1/2 A + 1/2 B = 1/2 (180°)
1/2 A + 1/2 B = 90° __【1】

Since, AP and PB are angle bisectors of A and B . Therefore,

Angle 1 = 1/2 A
Angle 2 = 1/2 B

Substitute the values in【1】,

Angle 1 + Angle 2 = 90°____【2】

Now, in ∆ APB,
1 + APB + 2 = 180°
90° + APB = 180°. [From 【2】]
APB = 90°
- HENCE PROVED

A relation R defined on the set A = {1,2,3,5} as {(x, y): x+y >10: x,y ∈ A} is
  • a)
    Empty relation
  • b)
    Universal relation
  • c)
    Zero relation
  • d)
    Identity relation
Correct answer is option 'A'. Can you explain this answer?

Gayatri Kumar answered
This relation R is not transitive.

To show this, we need to find a counterexample where the relation fails to hold for three elements in A.

Let's consider (1,2), (2,5), and (1,5). We know that (1,2) and (2,5) are in R, since 1 is less than 2 and 2 is less than 5. Similarly, (2,5) is in R because 2 is less than 5.

However, (1,5) is not in R since 1 is less than 5. Therefore, we have a counterexample where (1,2) and (2,5) are in R, but (1,5) is not. This shows that R is not transitive.

In a triangle, the line segment joining the midpoints of two sides has which of the following properties?
  • a)
    It is perpendicular to the third side.
  • b)
    It is equal in length to the third side.
  • c)
    It is parallel to the third side and half of its length.
  • d)
    It divides the triangle into two congruent triangles.
Correct answer is option 'C'. Can you explain this answer?

Imk Pathshala answered
Answer: C
Solution:
In a triangle, if a line segment joins the midpoints of two sides, it is parallel to the third side and half of its length. This is derived from the property of midpoints and parallelograms formed in the figure.
Correct Answer: (C) It is parallel to the third side and half of its length.

Which of the following statements correctly proves that each angle of a rectangle is a right angle?
  • a)
    Opposite angles of a rectangle are supplementary.
  • b)
    Interior angles on the same side of a transversal in a rectangle are always 90°.
  • c)
    A rectangle is a parallelogram where one angle is a right angle, and all opposite and adjacent angles are equal to 90°.
  • d)
    A rectangle does not follow the property of a parallelogram.
Correct answer is option 'C'. Can you explain this answer?

Imk Pathshala answered
Answer: C
Solution:
A rectangle is a parallelogram where one angle is a right angle (90 degrees). Using the properties of parallelograms:
  1. Interior angles on the same side of the transversal add up to 180 degrees
  2. Opposite angles are equal.
Since one angle is 90 degrees , all other angles (∠B,∠C,∠D)  are also 90 degrees
Correct Answer: (C) A rectangle is a parallelogram where one angle is a right angle, and all opposite and adjacent angles are equal to 90°.

AN and CP are perpendiculars to the diagonal BD of a parallelogram ABCD. Choose the correct option
  • a)
    AN ≠ CP
  • b)
    AN > CP
  • c)
    AN < CP
  • d)
    AN = CP
Correct answer is option 'D'. Can you explain this answer?

EduRev Class 9 answered
Here, AN and CP are perpendiculars dropped from points A and C, respectively, to the diagonal BD of the parallelogram ABCD.
From properties of parallelograms and the perpendiculars drawn from vertices to the diagonal, it can be concluded that the two perpendiculars AN and CP must be equal in length. This is because in any parallelogram, the perpendicular distances from opposite vertices to the diagonal are always equal.
Thus, the correct option is: d) AN = CP

Chapter doubts & questions for Functions - Mathematics for Grade 8 2025 is part of Grade 8 exam preparation. The chapters have been prepared according to the Grade 8 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Grade 8 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

Chapter doubts & questions of Functions - Mathematics for Grade 8 in English & Hindi are available as part of Grade 8 exam. Download more important topics, notes, lectures and mock test series for Grade 8 Exam by signing up for free.

Mathematics for Grade 8

34 videos|73 docs|17 tests

Top Courses Grade 8

© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup