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What is the slope of the line passing through points (-2, 4) and (4, 1)?
What is the slope of the line passing through points (-2, 4) and (4, 1)?
A line passes through the points (5, 6) and (5, -2). What is the slope of this line?
A line passes through the points (5, 6) and (5, -2). What is the slope of this line?
What is the slope of the line that passes through the points (-3, 2) and (7, 2)?
What is the slope of the line that passes through the points (-3, 2) and (7, 2)?
The equation of a line on a graph has a slope of 1/2 and crosses the y-axis at 3. Which of the following is the equation of this line?
The equation of a line on a graph has a slope of 1/2 and crosses the y-axis at 3. Which of the following is the equation of this line?
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A line has a slope of 1/2 and passes through the points (4, 6) and (m, -2). What is the value of m?
A line has a slope of 1/2 and passes through the points (4, 6) and (m, -2). What is the value of m?
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A line has a slope of -5/4 and passes through the points (3, 7) and (p, -4). What is the value of p?
A line has a slope of -5/4 and passes through the points (3, 7) and (p, -4). What is the value of p?
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Which equation below represents a line with a slope of 3, passing through the point (2, 5)?
Which equation below represents a line with a slope of 3, passing through the point (2, 5)?
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Which of these is the point-slope form of a line with a slope of -2, passing through the point (-1, 4)?
Which of these is the point-slope form of a line with a slope of -2, passing through the point (-1, 4)?
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Given the function f(x) representing the number of people at a tourist destination over time, what is the value of f(4)?
Given the function f(x) representing the number of people at a tourist destination over time, what is the value of f(4)?
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Which transformations are applied to the parent function f(x) = |x| to obtain the function h(x) = -3|x - 4| + 5? (Select all that apply)
Which transformations are applied to the parent function f(x) = |x| to obtain the function h(x) = -3|x - 4| + 5? (Select all that apply)
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If $f(x) = 3x + 2$ and $h(x) = x^2 - 1$, what is the value of $4[f(-2) + h(3)]$?
If $f(x) = 3x + 2$ and $h(x) = x^2 - 1$, what is the value of $4[f(-2) + h(3)]$?
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Given the function $f(x) = -2x + 3$, what is $f(3) - f(4)$?
Given the function $f(x) = -2x + 3$, what is $f(3) - f(4)$?
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Given a function, find the range if the domain is ${-2, 1, 3}$ where the function is defined by the following mappings: -2 maps to 3, 1 to 5 and 3 to 5. (Select the elements in the range)
Given a function, find the range if the domain is ${-2, 1, 3}$ where the function is defined by the following mappings: -2 maps to 3, 1 to 5 and 3 to 5. (Select the elements in the range)
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What is the result of $f(-1)$ when the function is defined by $f(x) = 3x^2 + 2$?
What is the result of $f(-1)$ when the function is defined by $f(x) = 3x^2 + 2$?
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If $g(x) = |x - 2| + 1$, what is the smallest possible value for $g(x)$?
If $g(x) = |x - 2| + 1$, what is the smallest possible value for $g(x)$?
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For $j(x) = rac{1}{2}x - 3$, what is $j(6) - j(2)$?
For $j(x) = rac{1}{2}x - 3$, what is $j(6) - j(2)$?
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Given the function $f(x) = x^3 + x^2 - 5$, what is the value of $f(2)$?
Given the function $f(x) = x^3 + x^2 - 5$, what is the value of $f(2)$?
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A function f(x) represents the distance from a house to a café over time. If you are given a graph of f(x), what does f(7.5) represent?
A function f(x) represents the distance from a house to a café over time. If you are given a graph of f(x), what does f(7.5) represent?
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How does the graph of $k(x) = 2|-x + 3| - 4$ transform the parent function?
How does the graph of $k(x) = 2|-x + 3| - 4$ transform the parent function?
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What is the equation for the nth term of the arithmetic sequence 10, 8, 6, 4, ...?
What is the equation for the nth term of the arithmetic sequence 10, 8, 6, 4, ...?
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Consider the function $k(x) = 2|-x + 3| - 4$ Identify all correct statements.
Consider the function $k(x) = 2|-x + 3| - 4$ Identify all correct statements.
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What is the 10th term in the arithmetic sequence 10, 8, 6, 4, …?
What is the 10th term in the arithmetic sequence 10, 8, 6, 4, …?
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Which equation represents the line passing through the point (-2, 3) with a slope of $\frac{3}{2}$?
Which equation represents the line passing through the point (-2, 3) with a slope of $\frac{3}{2}$?
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When the equation $y - 3 = 4(x + 2)$ is written in standard form $Ax + By = C$, what are the values of A, B, and C?
When the equation $y - 3 = 4(x + 2)$ is written in standard form $Ax + By = C$, what are the values of A, B, and C?
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Using the points (2007, 67.11) and (2016, 92.98), where x is the number of years since 2006, what is the equation of the line of fit in slope-intercept form?
Using the points (2007, 67.11) and (2016, 92.98), where x is the number of years since 2006, what is the equation of the line of fit in slope-intercept form?
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Based on the trend line calculated using points (2007, 67.11) and (2016, 92.98), what is the predicted price of a ticket in 2030?
Based on the trend line calculated using points (2007, 67.11) and (2016, 92.98), what is the predicted price of a ticket in 2030?
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Solve the inequality $-2y > 10$
Solve the inequality $-2y > 10$
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Which of the following inequalities has no solution?
Which of the following inequalities has no solution?
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Solve and graph the inequality $y - 3 > 1$.
Solve and graph the inequality $y - 3 > 1$.
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Which equation correctly represents a line with a slope of -3/4 and passes through the point (0, -7)?
Which equation correctly represents a line with a slope of -3/4 and passes through the point (0, -7)?
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Sophia sells 3 pancakes and a coffee for $7.50. She also sells 1 pancake and a coffee for $3.00. What is the cost of a single pancake?
Sophia sells 3 pancakes and a coffee for $7.50. She also sells 1 pancake and a coffee for $3.00. What is the cost of a single pancake?
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Using the same scenario, what is the cost of a single cup of coffee?
Using the same scenario, what is the cost of a single cup of coffee?
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BrightTalk Mobile charges $0.25 per minute plus a monthly fee. Sarah's bill was $45 for 150 minutes. Which equation can be used to solve for the monthly fee?
BrightTalk Mobile charges $0.25 per minute plus a monthly fee. Sarah's bill was $45 for 150 minutes. Which equation can be used to solve for the monthly fee?
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Using the BrightTalk Mobile scenario, what is the monthly base fee?
Using the BrightTalk Mobile scenario, what is the monthly base fee?
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If a line has a slope of $m = -\frac{4}{3}$ and passes through a point $(0, -7)$, which of the following represents its equation in point-slope form?
If a line has a slope of $m = -\frac{4}{3}$ and passes through a point $(0, -7)$, which of the following represents its equation in point-slope form?
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What do the $x$ and $y$ variables represent when making equations to determine the costs of pancakes and coffee?
What do the $x$ and $y$ variables represent when making equations to determine the costs of pancakes and coffee?
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If the point slope form of an equation is $y - y_1 = m(x - x_1)$, and the equation is transformed to $y + 7 = -\frac{3}{4}(x + 0)$, what is the slope and point from the transformed equation?
If the point slope form of an equation is $y - y_1 = m(x - x_1)$, and the equation is transformed to $y + 7 = -\frac{3}{4}(x + 0)$, what is the slope and point from the transformed equation?
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Which of the following inequalities has (7, 0) as a solution?
Which of the following inequalities has (7, 0) as a solution?
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What is the solution to the inequality $|4x - 7| > 11$?
What is the solution to the inequality $|4x - 7| > 11$?
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Which of the following represents a line parallel to the x-axis?
Which of the following represents a line parallel to the x-axis?
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Which of the following operations would eliminate 'y' in the system of equations: $8x - 9y = 13$ and $16x + 3y = 22$?
Which of the following operations would eliminate 'y' in the system of equations: $8x - 9y = 13$ and $16x + 3y = 22$?
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Given the system of equations $c - \frac{3}{4}d = 6$ and $c = 4d - 8$, what is the value of 'c' when solved using substitution?
Given the system of equations $c - \frac{3}{4}d = 6$ and $c = 4d - 8$, what is the value of 'c' when solved using substitution?
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Given the system of equations: $\frac{1}{4}f - \frac{1}{3}e = 7$ and $-\frac{1}{3}e + \frac{1}{2}f = 9$. What is the value of 'f' when solved using elimination?
Given the system of equations: $\frac{1}{4}f - \frac{1}{3}e = 7$ and $-\frac{1}{3}e + \frac{1}{2}f = 9$. What is the value of 'f' when solved using elimination?
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Two lines are parallel. Line 1 includes points (1, 3) and (4, 7), and Line 2 includes points (x, 10) and (2, 6). What is the value of x?
Two lines are parallel. Line 1 includes points (1, 3) and (4, 7), and Line 2 includes points (x, 10) and (2, 6). What is the value of x?
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Study Notes
Module 3: Relations and Functions
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Function of Time (f(x)): The number of people at a tourist destination varies with the month. f(4) = 5 (people)
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Transformations of Functions (h(x)): h(x) = -3|x-4|+5. This function is a transformation of the absolute value function, f(x) = |x|. The transformations include a vertical stretch by a factor of 3, translated right 4 units, and translated up 5 units
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Function Evaluation (f(x) and h(x)): Given f(x)=3x+2 and h(x)=x2 - 1, find 4[f(-2)+h(3)]
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f(-2)=-4
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h(3)=8
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4(-4 + 8) = 16
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Function Difference (f(x)): For f(x)=-2x+3, calculate f(3)-f(4)=-3-(-5) = 2.
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Range of Function: Given a function f(x)=x3+x-5/3 and a domain of {-2, 1, 3}, find the range.
- f(-2) = -15
- f(1) = -3
- f(3) = 25 Range: {-15, -3, 25}
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Function of Time (f(x)): f(7.5)=7.5
Module 4: Linear and Nonlinear Functions
- Slope of a Line: The slope of a line passing through (-3, 5) and (3, 6) is 1/6.
- Slope of a Line: The slope of a line passing through (-3, 2) and (7, 2) is 0.
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Identifying Equations of Straight Lines from Graphs:
- Recognize that the slope-intercept form of a line is y = mx + b.
- Calculate the slope by identifying two distinctive points (e.g., x-intercept and y-intercept).
- Determine the y-intercept (the value where the line intersects the y-axis).
- Formulate the equation.
Module 5: Creating Linear Equations
- Finding Monthly Base Fee: Given Sarah's phone bill in August was $45 for 150 minutes, and charges are $0.25 per minute, the monthly base fee = $7.50.
- Phone Bill Calculation: For 180 minutes in September, the total cost is $52.50.
Module 6: Linear Inequalities
- Solving Inequalities: Solve -2y>10 to get y < -5.
- Inequalities with No Solutions: Some inequalities have no solution. For example, inequalities like 3x+5<3x+7 or 5x+82<-5(x+2) have no solution
- Solve and Graph Inequality: Solve -8y<-3y+5, to get y > -1.
Module 7: Systems of Equations and Inequalities
- Parallel Line: A line parallel to the x-axis will have the equation y=b
- Solving Systems of Equations: Various methods exist to solve systems of equations, including substitution or elimination.
- Point-Slope Form: Equations of lines can be represented in various forms such as point-slope form (y-y1 = m(x-x1))
- Perpendicular Lines: Perpendicular lines have slopes that are negative reciprocals of each other (e.g., if one slope is m, the other is -1/m)
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Description
This quiz focuses on key concepts in relations and functions from Algebra Module 3 and 4. Topics include function evaluation, transformations, and the calculation of slopes for linear and nonlinear functions. Test your understanding and application of these mathematical principles.
