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Questions and Answers
Which type of function is represented by $f(x) = (x + 1)^3 - (x - 1)^3$?
Which type of function is represented by $f(x) = (x + 1)^3 - (x - 1)^3$?
What is the point of intersection of the equations $3x - y = 4$ and $x + y = 8$?
What is the point of intersection of the equations $3x - y = 4$ and $x + y = 8$?
If the ordered pairs $(a + 2, 4)$ and $(5, 2a + b)$ are equal, what are the values of a and b?
If the ordered pairs $(a + 2, 4)$ and $(5, 2a + b)$ are equal, what are the values of a and b?
If {(a,8),(6,b)} represents an identity function, what are the values of a and b?
If {(a,8),(6,b)} represents an identity function, what are the values of a and b?
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What is the sum of the exponents of the prime factors in the prime factorization of 1729?
What is the sum of the exponents of the prime factors in the prime factorization of 1729?
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Study Notes
Function Representation
- The function $f(x) = (x + 1)^3 - (x - 1)^3$ can be simplified to represent a polynomial function.
- Through algebraic expansion, it resolves to $f(x) = 6x$.
- The function is linear, indicating a constant rate of change.
Intersection of Equations
- The equations $3x - y = 4$ and $x + y = 8$ can be solved simultaneously.
- By rearranging to express $y$, substituting, and solving yields the intersection point $(4, 4)$.
Equal Ordered Pairs
- In the pairs $(a + 2, 4)$ and $(5, 2a + b)$, both components must be equal.
- Setting $a + 2 = 5$ leads to $a = 3$.
- For the second component $4 = 2a + b$, substituting $a = 3$ results in $b = -2$.
- The values of $a$ and $b$ are $3$ and $-2$, respectively.
Identity Function Characteristics
- An identity function maps each element to itself; thus, the pairs must satisfy $a = 6$ and $b = 8$.
- This means that for the identity function to hold true, $a$ must equal $6$ and $b$ must equal $8$.
Prime Factorization of 1729
- The prime factorization of 1729 is $7^1 \times 13^1 \times 19^1$.
- The sum of the exponents in this factorization is $1 + 1 + 1 = 3$.
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Description
Test your knowledge of math functions and ordered pairs with this quiz. Questions cover topics such as identifying function types, finding points of intersection, and solving for ordered pairs.
