The graph given below represents which of the following function? Option 1: y = x + 1 Option 2: y =, x + 1, + 1 Option 3: y =, x - 1, + 1 Option 4: y =, x + 1, - 1

Answer: y =, x - 1, + 1. Solution: The graph shows a V-shaped curve, which is characteristic of an absolute value function. The vertex is the lowest point where the two lines meet. From the graph, the vertex is at the point (1, 1). For any absolute value function in the form y =, x - h, + k, the vertex is at the point (h, k). In this form: - h moves the graph left or right - k moves the graph up or down Since the vertex is at (1, 1): h = 1 k = 1 Substituting into the formula: y =, x - 1, + 1 The sign inside the absolute value is opposite to the vertex location: - y =, x - 1, has vertex at x = 1 (moves right) - y =, x + 1, has vertex at x = -1 (moves left) This is because x - 1 = 0 gives x = 1. Therefore, the answer is y =, x - 1, + 1

Algebra

Relations & Functions

Medium

applied

The graph given below represents which of the following function?

$y = |x + 1|$

$y = |x + 1| + 1$

$y = |x - 1| + 1$

$y = |x + 1| - 1$

✅ Correct Option: 3

The graph shows a V-shaped curve, which is characteristic of an absolute value function.

The vertex is the lowest point where the two lines meet.

From the graph, the vertex is at the point $(1, 1)$ .

For any absolute value function in the form $y = |x - h| + k$ , the vertex is at the point $(h, k)$ .

In this form:

$h$ moves the graph left or right
$k$ moves the graph up or down

Since the vertex is at $(1, 1)$ :

$h = 1$

$k = 1$

Substituting into the formula:

$y = |x - 1| + 1$

The sign inside the absolute value is opposite to the vertex location:

$y = |x - 1|$ has vertex at $x = 1$ (moves right)
$y = |x + 1|$ has vertex at $x = -1$ (moves left)

This is because $x - 1 = 0$ gives $x = 1$ .

Therefore, the answer is $y = |x - 1| + 1$

2025: 16 May Shift 1

If R and S are two equivalence relations on a set A, then

2022: 10 Aug Shift 1

A. A relation $R$ on a set $A$ is called an equivalence relation, if it is reflexive, symmetric and transitive.

B. The function $f : R \to R$ defined by $f(x) = e^x$ is not one-one.

C. The one-one function is also known as injective function.

D. The onto function is also known as subjective function.

E. A function $f : X \to Y$ is said to be many-one, if two or more than two elements in set $X$ have the different image in set $Y$ .

Choose the correct answer from the option given below:

2022: 30 Aug Shift 1

If $R$ is a relation on $Z$ (set of all integers) defined by $xRy$ , iff $|x - y| \leq 1$ , then

(a) $R$ is reflexive

(b) $R$ is symmetric

(d) $R$ is not symmetric

(e) $R$ is not transitive

Choose the most appropriate answer from the options given below

2025: 16 May Shift 1

Match List-I with List-II

Where ℝ is set of real numbers

List-I	List-II
(A) f: ℝ → ℝ s.t f(x) = x⁴ is	(I) one-one, Into
(B) f: ℝ → [0, ∞) s.t f(x) = x⁴ is	(II) many-one, into
(C) f: [0, ∞) → ℝ s.t f(x) = x⁴ is	(III) one-one, onto
(D) f: [0, ∞) → [0, ∞) s.t f(x) = x⁴ is	(IV) many-one, onto

Choose the correct answer from the options given below:

2026: 29 May Shift 2

Match the LIST-I with LIST-II (Consider N and R as set of natural numbers and set of real numbers respectively)

	LIST-I Function		LIST-II
A.	$f: N \to N, f(x) = x^2$ is	I.	Neither one-one nor onto
B.	$f: R \to R, f(x) = 3 - 2x$ is	II.	one-one but not onto
C.	$f: R \to R, f(x) = x^2$ is	III.	onto but not one-one
D.	$f: \{-1,1\} \to \{1\}, f(x) = \vert x \vert$ is	IV.	one-one and onto

Choose the correct answer from the options given below:

2026: 18 May Shift 1

If $A = \{x: x \in R, -\frac{\pi}{2} \leq x \leq \frac{\pi}{2}\}$ and $B = \{y: y \in R, -1 \leq y \leq 1\}$ and function $f: A \rightarrow B$ defined by $f(x) = \sin x$ , then $f$ is

The graph given below represents which of the following function?

Solution

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