Algebra Test on Sets and Functions

Questions and Answers

How many subsets does set A have if the set A has 3 elements?

If A = {1, 3, 5} and B = {1, 2, 3, 4, 5, 6} then A ∪ B equals?

{1, 2, 3, 4, 5, 6}

Given A = {1, 3, 5}, B = {2, 4, 6}, and C = {1, 2, 3, 4, 5, 6}, then A ∪ (B ∩ C) equals?

{1, 2, 3, 4, 5, 6}

Select all that justify the statement: 3 + (y + 5) = y + 8.

Commutative - addition Signup and view all the answers

Select all that justify the statement: 2 * 1/2 = 1.

Inverse - multiplication Signup and view all the answers

Select all that justify the statement: 8 * 1/8 + (-1) + 5 = 5.

Inverse - multiplication Signup and view all the answers

Select all that justify the statement: 10 + x * 12 = 12x + 10.

Commutative - addition Signup and view all the answers

If ƒ = {(5, 1),(6, 2),(7, 3),(8, 1),(9, 7)}, then the range of ƒ is?

{1, 2, 3, 7} Signup and view all the answers

The inverse of a function is a function.

False Signup and view all the answers

Given that ƒ(x) = x² + 5x, evaluate ƒ(-2).

-6 Signup and view all the answers

Evaluate g(3) if g(x) = 2x + 1.

7 Signup and view all the answers

If F(x) = x² + 5x and G(x) = 2x + 1, find F(5) + G(6).

63 Signup and view all the answers

If g(x) = 2x + 1, find g(a + h) - g(a).

2h Signup and view all the answers

Simplify the expression in exponential notation: a * a * a.

a^3 Signup and view all the answers

Simplify the expression in exponential notation: 2 * a * b * a * b.

2a^2b^2 Signup and view all the answers

The expression 3x² represents?

(3)(x)(x) Signup and view all the answers

(3a)^3 = This expression without exponents is?

3a3a3a Signup and view all the answers

(abc)^2 = This expression without exponents is?

abcabc or aabbcc Signup and view all the answers

Express in simplified exponential notation: x^3 * x^5 = ?

x^8 Signup and view all the answers

In simplified exponential notation, the expression a^2 * a^-3 * a = ?

1 Signup and view all the answers

Express in simplified exponential notation: 18a^3b^2 / 2ab = ?

9a^2b Signup and view all the answers

Evaluate each expression: 3^-2 = ?

1/9 Signup and view all the answers

Simplify: 5(x - 2) + 3x.

8x - 10 Signup and view all the answers

Simplify: 7 - 2(5 - 2x).

4x - 3 Signup and view all the answers

Simplify: 3(x + 2) + 4(x - 5).

7x - 14 Signup and view all the answers

Study Notes

Subsets and Union

A set with 3 elements has a total of 8 subsets.
The union of sets A = {1, 3, 5} and B = {1, 2, 3, 4, 5, 6} results in the set {1, 2, 3, 4, 5, 6}.
For sets A = {1, 3, 5}, B = {2, 4, 6}, and C = {1, 2, 3, 4, 5, 6}, A ∪ (B ∩ C) equals {1, 2, 3, 4, 5, 6}.

Algebraic Justifications

The equation 3 + (y + 5) = y + 8 is justified by the commutative and associative properties of addition.
For the equation 2 × 1/2 = 1, the justification lies in the inverse property of multiplication.
The equation 8 × 1/8 + (-1) + 5 = 5 is supported by the inverse properties of addition and multiplication.
10 + x × 12 = 12x + 10 relies on the commutative properties of addition and multiplication.

Functions and Evaluations

The range of the function f = {(5, 1), (6, 2), (7, 3), (8, 1), (9, 7)} is {1, 2, 3, 7}.
The inverse of a function can sometimes be a function.
For f(x) = x² + 5x, evaluating f(-2) yields -6.
If g(x) = 2x + 1, then g(3) = 7.
F(5) + G(6) results in 63, where F(x) = x² + 5x and G(x) = 2x + 1.
Finding g(a + h) - g(a) for g(x) results in 2h.

Exponential Notation

The expression a × a × a simplifies to a³.
The expression 2 × a × b × a × b simplifies to 2a²b².
3x² represents the product of (3)(x)(x).
The expression (3a)³ expands to 3aaa.
(abc)² expands to abcabc or aabbcc.
The expression x³ × x⁵ simplifies to x⁸.
The expression a² × a⁻³ × a simplifies to 1.
The algebraic expression (18a³b²) / (2ab) simplifies to 9a²b.
Evaluating 3⁻² gives 1/9.

Simplification of Algebraic Expressions

The expression 5(x - 2) + 3x simplifies to 8x - 10.
7 - 2(5 - 2x) simplifies to 4x - 3.
3(x + 2) + 4(x - 5) simplifies to 7x - 14.

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Description

Test your understanding of sets, structures, and functions with this algebra quiz. The questions cover topics such as subsets, unions, and equations. Ideal for students looking to reinforce their knowledge in algebraic concepts.