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Given an arithmetic sequence where the first term is -8 and the common difference is 6, what is the explicit formula?
Given an arithmetic sequence where the first term is -8 and the common difference is 6, what is the explicit formula?
In the arithmetic sequence 7, 4, 1, ..., what is the value of the seventh term ($a_7$)?
In the arithmetic sequence 7, 4, 1, ..., what is the value of the seventh term ($a_7$)?
A piecewise function is defined as follows: $f(x) = \begin{cases} 3x - 1, & x < 1 \ x + 2, & x \geq 1 \end{cases}$. What is the value of f(-2)?
A piecewise function is defined as follows: $f(x) = \begin{cases} 3x - 1, & x < 1 \ x + 2, & x \geq 1 \end{cases}$. What is the value of f(-2)?
A dataset of Olympic 500-meter Gold Medal Speed Skating times is analyzed. Which of the following is a valid interpretation regarding causality?
A dataset of Olympic 500-meter Gold Medal Speed Skating times is analyzed. Which of the following is a valid interpretation regarding causality?
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Given $p(x) = \frac{10}{x-3}$, what is the value of $p(5)$?
Given $p(x) = \frac{10}{x-3}$, what is the value of $p(5)$?
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If $p(x) = \frac{10}{x-3}$ and $p(x) = 13$, what is the value of x?
If $p(x) = \frac{10}{x-3}$ and $p(x) = 13$, what is the value of x?
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A function $f(x)$ is shifted 2 units up, resulting in a new function $g(x)$. What change will happen to the original function $f(x)$?
A function $f(x)$ is shifted 2 units up, resulting in a new function $g(x)$. What change will happen to the original function $f(x)$?
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A data set shows the number of graduating 8th graders from a middle school since 2012. Using linear regression analysis, a correlation coefficient of 0.92 is found. Which statement below accurately interprets this value?
A data set shows the number of graduating 8th graders from a middle school since 2012. Using linear regression analysis, a correlation coefficient of 0.92 is found. Which statement below accurately interprets this value?
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Which of the following relations is a function?
Which of the following relations is a function?
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A function is defined as $y = 4x + 3$. Which of the following points lies on its graph?
A function is defined as $y = 4x + 3$. Which of the following points lies on its graph?
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Ms. Yi tutors after work for x hours. Which is the most reasonable domain for the 'x' in this context?
Ms. Yi tutors after work for x hours. Which is the most reasonable domain for the 'x' in this context?
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Gary starts with 25 Pokemon cards and gets 3 more each week. Given n represents the number of weeks, which explicit formula describes this?
Gary starts with 25 Pokemon cards and gets 3 more each week. Given n represents the number of weeks, which explicit formula describes this?
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Given the mapping: {-7 -> 2, 0 -> 2, 3 -> 1}, what is the range of this relation?
Given the mapping: {-7 -> 2, 0 -> 2, 3 -> 1}, what is the range of this relation?
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Given the mapping: {-7 -> 2, 0 -> 2, 3 -> 1}, is this relation a function?
Given the mapping: {-7 -> 2, 0 -> 2, 3 -> 1}, is this relation a function?
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Which of the following equations represents a line with a slope of $1/4$ ?
Which of the following equations represents a line with a slope of $1/4$ ?
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What is the y-intercept of the line represented by the equation $f(x) = \frac{1}{4}x - 3$?
What is the y-intercept of the line represented by the equation $f(x) = \frac{1}{4}x - 3$?
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Which of the following relations represents a function?
Which of the following relations represents a function?
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Which function corresponds to the table with values (0,-5), (1,-3), (2,-1), (3,1)?
Which function corresponds to the table with values (0,-5), (1,-3), (2,-1), (3,1)?
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Ms. Yi tutors her friends' children for x hours after school on Wednesdays. Which of the following is the most reasonable domain for x?
Ms. Yi tutors her friends' children for x hours after school on Wednesdays. Which of the following is the most reasonable domain for x?
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Gary starts with 25 Pokémon cards and gets 3 new cards per week. Which arithmetic sequence describes the number of cards he has after n weeks?
Gary starts with 25 Pokémon cards and gets 3 new cards per week. Which arithmetic sequence describes the number of cards he has after n weeks?
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Given a mapping with the following ordered pairs: {(1, 2), (2, 4), (3, 6), (4, 8)}, what is the corresponding range?
Given a mapping with the following ordered pairs: {(1, 2), (2, 4), (3, 6), (4, 8)}, what is the corresponding range?
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For the function $f(x) = \frac{1}{2}x - 3$, what is the value of $f(6)$?
For the function $f(x) = \frac{1}{2}x - 3$, what is the value of $f(6)$?
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A function is defined by the rule $y = 4x - 7$. If the input x is 5, what is output y?
A function is defined by the rule $y = 4x - 7$. If the input x is 5, what is output y?
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Which of the following is the explicit formula for an arithmetic sequence?
Which of the following is the explicit formula for an arithmetic sequence?
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Given the function $f(x)$, where $f(-6) = -12$ and $f(4) = 3$, and $g(x)$ is $f(x)$ shifted 2 units up, what is the function for $g(x)$?
Given the function $f(x)$, where $f(-6) = -12$ and $f(4) = 3$, and $g(x)$ is $f(x)$ shifted 2 units up, what is the function for $g(x)$?
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What is the explicit formula, using distribution, for the arithmetic sequence -8, -2, 4, 10, ...?
What is the explicit formula, using distribution, for the arithmetic sequence -8, -2, 4, 10, ...?
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Given the piecewise function: $f(x) = \begin{cases} 3x^2 - 1, & x < 1 \ 0, & x = 1 \ x + 2, & x \geq 1 \end{cases}$, find $f(-2)$.
Given the piecewise function: $f(x) = \begin{cases} 3x^2 - 1, & x < 1 \ 0, & x = 1 \ x + 2, & x \geq 1 \end{cases}$, find $f(-2)$.
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Based on the provided information, which best describes the correlation of the Olympic 500-meter Gold Medal Speed Skating times?
Based on the provided information, which best describes the correlation of the Olympic 500-meter Gold Medal Speed Skating times?
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Given the function $p(x) = \frac{x}{8}+ \frac{3}{4}$, what is the value of $p(5)$?
Given the function $p(x) = \frac{x}{8}+ \frac{3}{4}$, what is the value of $p(5)$?
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For the function $p(x) = \frac{x}{8} + \frac{3}{4}$, if $p(x) = 13$, what is the value of x?
For the function $p(x) = \frac{x}{8} + \frac{3}{4}$, if $p(x) = 13$, what is the value of x?
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A set of data shows the number of graduating 8th graders from a middle school since 2012. The linear regression equation is $y = 9.17x - 18114.68$, and the correlation coefficient is 0.99. What does the correlation coefficient mean in this context?
A set of data shows the number of graduating 8th graders from a middle school since 2012. The linear regression equation is $y = 9.17x - 18114.68$, and the correlation coefficient is 0.99. What does the correlation coefficient mean in this context?
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Study Notes
Arithmetic Sequences
- Explicit formula: an = a1 + (n − 1)d
- an represents the nth term
- a1 is the first term
- n is the term number
- d is the common difference
Functions
- A relation is a function if each input (x-value) has only one output (y-value).
- Verifying if a relation is a function:
- Check if any x-values are repeated in the relation. If an x-value is repeated, and the y-values are different, the relation is not a function.
Function Tables
- Given a function rule, a function table lists corresponding input (x) and output (y) values.
Domains
- The domain of a function is the set of all possible input values (x-values).
- Reasonable domains often consider practical limitations or restrictions.
Arithmetic Sequences (Example)
- If Gary starts with 25 cards and gets 3 more each week, the number of cards after n weeks can be described by an arithmetic sequence:
- A(n) = 25 + (n - 1) * 3
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Description
This quiz covers key concepts in algebra related to arithmetic sequences and functions. You'll explore explicit formulas, function verification, function tables, and the definition of domains. Test your understanding of these essential topics in algebra!
