Which among the following relations between X - y doesn-t represent a functionA- x -12- y -32-52- x -4-6- y - RB- y 2-4 x - x -0- - y - RC- x 2-4 y - x - y - RD- y -2 x -52- x - y - R

The correct options are A (x 1)^2+(y 3)^2=5^2 ,x ∈ [ 4,6] , y∈ℝ B y^2=4x, x∈ [0,∞), y∈ nbsp;ℝ nbsp; We know that if a vertical line parallel to y axis for t ...

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Standard XII

Mathematics

Definition of Function

Which among t...

Question

Which among the following relations between $x, y$ doesn't represent a function

(x - 1)^{2} + (y - 3)^{2} = 5^{2}, x \in [- 4, 6], y \in R

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y^{2} = 4 x, x \in [0, \infty), y \in R

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x^{2} = 4 y, x, y \in R

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y = 2 x + 5^{2}, x, y \in R

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Solution

The correct options are
A $(x - 1)^{2} + (y - 3)^{2} = 5^{2}, x \in [- 4, 6], y \in R$
B $y^{2} = 4 x, x \in [0, \infty), y \in R$
We know that if a vertical line parallel to $y$ axis for the curve cuts the graph at one point then it represents a functionHere vertical line cuts the graph at more than one point
$∴$ It is not a function

Vertical line is cutting the graph at more than one point
$∴$ It is not a function

Vertical line is cutting the graph at one point

$∴$ It is a function

Vertical line is cutting the graph at one point only.

$∴$ It is a function

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Similar questions

Q. If

\frac{3}{x + y} + \frac{2}{x - y} = 2 and \frac{9}{x + y} - \frac{4}{x - y} = 1

then
(a)

x = \frac{1}{2}, y = \frac{3}{2}

(b)

x = \frac{5}{2}, y = \frac{1}{2}

(c)

x = \frac{3}{2}, y = \frac{1}{2}

(d)

x = \frac{1}{2}, y = \frac{5}{2}

Q. The equation of the image of circle

x^{2} + y^{2} - 2 x - 4 y = 0

in the line

3 x - 4 y + 30 = 0

Q. Which of the following are functions?

(a) {(x, y) : y² = x, x, y ∈ R}
(b) {(x, y) : y = |x|, x, y ∈ R}
(c) {(x, y) : x² + y² = 1, x, y ∈ R}
(d) {(x, y) : x² − y² = 1, x, y ∈ R}

Which one of the following is not a function ?

(a) ${(x, y) : x, y ϵ R, x^{2} = y}$
(b) ${(x, y) : x, y ϵ R, y^{2} = x}$
(c) ${(x, y) : x, y ϵ R, x = y^{3}}$
(d) ${(x, y) : x, y ϵ R, y = x^{3}}$

Q. Which one of the following is not a function?

(a) {(x, y) : x, y ∈ R, x² = y}
(b) {(x, y) : x, y ∈, R, y² = x}
(c) {(x, y) : x, y ∈ R, x² = y³}
(d) {(x, y) : x, y ∈, R, y = x³}

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Definition of Function

Standard XII Mathematics

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Which among the following relations between x,y doesn't represent a function

Which among the following relations between $x, y$ doesn't represent a function