Questions and Answers
The price of a ticket for an eight-year-old child is $8.
False
Find the slope of the line graphed above.
-6
Simplify the algebraic expression: x(x + 3) + x(2x - 4) + 6.
3x^2 - x + 6
What is the base fare for a taxi in Chicago?
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Select the graph of the piecewise function given by: ƒ(x) = 0 for 0 ≤ x < 4, ƒ(x) = 3 for 4 ≤ x < 8, ƒ(x) = 6 for 8 ≤ x < 12.
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How much weight did Sue lose each month?
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Which function ƒ(x) is represented in the table of apple costs?
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Which table correctly lists the three solutions for the equation 5x + y = 14?
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What expression represents the amount of money that Mary has raised?
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What linear equation represents how much Martina collects for one night of stay?
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Select the graph that displays the function ƒ(x) = -√x - 4.
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Write 9x + 3y = 15 in slope-intercept form.
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Use a table of values to graph the function ƒ(x) = √x.
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Which function ƒ(x) is represented in the table of moped rental costs?
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What expression is equivalent to 3(x - 6) + 5(x - 4)?
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Select the correct graph for the function ƒ(x) = -x - 7.
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How much would a customer pay to rent a golf cart for 4 hours?
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Which expression is equivalent to 9x - 3y - 5x + 7y + x + y?
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Select the correct graph for the function ƒ(x) = the cube root of x.
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Select the correct equation for the resulting function if ƒ(x) = the cube root of x is translated 3 units in the negative y-direction and 8 units in the negative x-direction.
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Study Notes
Admission Prices
- Theme park tickets vary based on children's ages.
- False statement regarding the price for an eight-year-old child at $8.
Slope Calculation
- Slope of the given line is -6.
Algebraic Expression Simplification
- Simplification of x(x + 3) + x(2x - 4) results in 3x² - x + 6.
Taxi Fare in Chicago
- Base fare for taxis is $3.50, with an addition of $2 per mile.
- Graph depicting this relationship should have a y-intercept at 3.5.
Piecewise Function Representation
- Piecewise function defined as:
- ƒ(x) = 0 for 0 ≤ x < 4
- ƒ(x) = 3 for 4 ≤ x < 8
- ƒ(x) = 6 for 8 ≤ x < 12
- Correct graphical representation aligns with the specified intervals and values.
Sue’s Weight Loss
- Sue lost consistent weight of 2 kg each month, starting from 82 kg.
Apples Cost Function
- Cost of apples represented by function ƒ(x) = 2x.
Solutions for Linear Equation
- Solutions to the equation 5x + y = 14 include (-1, 19), (0, 14), and (1, 9).
Mary’s Fundraising Expression
- Amount raised from chocolate bars is expressed as 3m + 4c, where m and c denote quantities of each type sold.
Martina’s Room Rental Equation
- Total collected for room rental can be calculated with the equation c = 25 + 10p + 5h, accounting for base fee, extra persons, and late checkout fees.
Function Graph Reflection
- Function ƒ(x) = -√x - 4 exhibits x-axis reflection and negative vertical shift.
Slope-Intercept Form
- Converting 9x + 3y = 15 to slope-intercept form yields y = -3x + 5.
Graph of Square Root Function
- Correct points for graphing ƒ(x) = √x include (1,1), (4,2), and (9,3).
Moped Rental Function
- Cost function for renting a moped represented as ƒ(x) = 0.5x + 10.
Expression Simplification
- Equivalent expression for 3(x - 6) + 5(x - 4) simplifies to 8x - 38.
Linear Function Representation
- Correct graph for function ƒ(x) = -x - 7 is labeled as A.
Golf Cart Rental Cost
- Total payment for 4 hours of renting a golf cart costs $73, computed as c = 12h + 25.
Additional Expression Simplification
- The expression 9x - 3y - 5x + 7y + x + y simplifies to 5x + 5y.
Reflection and Stretching of Function
- Upon reflection across the x-axis and vertical stretching by a factor of 2, the function ƒ(x) = √x transforms with significant coordinate changes.
Translation of Cube Root Function
- New function after a 3-unit downward and 8-unit leftward translation: ƒ(x) = ∛(x + 8) - 3.
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Test your knowledge of key concepts from Algebra 2 Lesson 1 with these flashcards. Covering topics like algebraic expressions and functions related to real-world applications, this quiz provides an engaging way to learn. Perfect for students looking to reinforce their understanding of algebra concepts.
