Relations and Functions Quiz

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Considering the relation R defined on set A = {a, b, c, d, e, f, g, h} with R = {(a, b), (b, b), (a, g), (b, a), (b, g), (g, a), (g, b), (g, g), (b, b)}, which of the following statements is true?

The domain and range of R are equal.

R is not a relation on A. (correct)

R is a proper subset of A x A.

R contains all possible ordered pairs in A x A.

For the relation R defined on set A = {1, 2, 3, 4, 6} by {(a, b) : a, b ∈ A and b is exactly divisible by a}, which statement about the relation R is correct?

The relation R is reflexive.

The relation R does not contain the pair (6, 3).

The relation R contains the pair (4, 6). (correct)

The relation R is symmetric.

In the relation R on set A = {1, 2, 3, 4, 6} where R = {(6, 3), (6, 2), (4, 2)}, what can be said about the domain and range of R?

The domain of R is {6} and the range of R is {2, 3}. (correct)

The domain of R is {2, 3} and the range of R is {2, 3}.

The domain of R is {4, 6} and the range of R is {2}.

The domain of R is {2, 3} and the range of R is {6}.

If (x + 1, y - 2) = (3, 1), which of the following statements is true?

x = 4 and y = 3. Signup and view all the answers

Given f(x) = $\frac{x-2}{1+(x-2)^3}$ and g(x) = $\frac{x-2}{1+(x-2)^3}$ with x ≠ 2, what can be concluded about f + g?

$\frac{x-2}{1+(x-2)^3}$ Signup and view all the answers

For functions f and g where f(x) = $\frac{2x}{x}$ if x ≥ 0 and f(x) = $0$ if x < 0 and g(x) = $0$ if x ≥ 0 and g(x) = $2x$ if x < 0, which statement is true about f - g?

$\frac{2}{x}$ if x ≥ 0 and $\frac{1}{2x}$ if x < 0 Signup and view all the answers

In the relation R on set A = {0, 8, -8} given by {(0, 8), (0, -8), (8, 0), (-8, 0)}, which of the following properties does the relation R possess?

Symmetric Signup and view all the answers

$A \times B$ for sets $A = {1, 3, 5}$ and $B = {2, 3}$ is given by:

${(1,2), (1,3), (5,2), (5,3)}$ Signup and view all the answers

$B \times A$ for sets $A = {1, 2, 3}$ and $B = {2, 3, 5}$ yields:

${(1,2), (2,3), (5,3)}$ Signup and view all the answers

$f + g$ for functions $f$ and $g$ defined as $f(x) = x^2$ for $x > 0$ and $g(x) = -x^2$ for $x < 0$ results in:

$f + g = x^2 - x^2$ Signup and view all the answers

Given the function $f(x) = |x - 4|$ over its domain, what is the range of the function?

[0,infinity] Signup and view all the answers

Relations and Functions Quiz

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Questions and Answers

Considering the relation R defined on set A = {a, b, c, d, e, f, g, h} with R = {(a, b), (b, b), (a, g), (b, a), (b, g), (g, a), (g, b), (g, g), (b, b)}, which of the following statements is true?

For the relation R defined on set A = {1, 2, 3, 4, 6} by {(a, b) : a, b ∈ A and b is exactly divisible by a}, which statement about the relation R is correct?

In the relation R on set A = {1, 2, 3, 4, 6} where R = {(6, 3), (6, 2), (4, 2)}, what can be said about the domain and range of R?

If (x + 1, y - 2) = (3, 1), which of the following statements is true?

Given f(x) = $\frac{x-2}{1+(x-2)^3}$ and g(x) = $\frac{x-2}{1+(x-2)^3}$ with x ≠ 2, what can be concluded about f + g?

For functions f and g where f(x) = $\frac{2x}{x}$ if x ≥ 0 and f(x) = $0$ if x < 0 and g(x) = $0$ if x ≥ 0 and g(x) = $2x$ if x < 0, which statement is true about f - g?

In the relation R on set A = {0, 8, -8} given by {(0, 8), (0, -8), (8, 0), (-8, 0)}, which of the following properties does the relation R possess?

$A \times B$ for sets $A = {1, 3, 5}$ and $B = {2, 3}$ is given by:

$B \times A$ for sets $A = {1, 2, 3}$ and $B = {2, 3, 5}$ yields:

$f + g$ for functions $f$ and $g$ defined as $f(x) = x^2$ for $x > 0$ and $g(x) = -x^2$ for $x < 0$ results in:

Given the function $f(x) = |x - 4|$ over its domain, what is the range of the function?

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