Algebra 2 Lesson 1 Flashcards

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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?

$3.50 Signup and view all the answers

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.

B. (closed 0 to open 4, 0) (closed 4 to open 8, 3) (closed 8 to open 12, 6) Signup and view all the answers

How much weight did Sue lose each month?

2 kg Signup and view all the answers

Which function ƒ(x) is represented in the table of apple costs?

ƒ(x) = 2x Signup and view all the answers

Which table correctly lists the three solutions for the equation 5x + y = 14?

(-1, 19) (0, 14) (1, 9) Signup and view all the answers

What expression represents the amount of money that Mary has raised?

3m + 4c Signup and view all the answers

What linear equation represents how much Martina collects for one night of stay?

c = 25 + 10p + 5h Signup and view all the answers

Select the graph that displays the function ƒ(x) = -√x - 4.

C. x-axis reflection, negative vertical shift Signup and view all the answers

Write 9x + 3y = 15 in slope-intercept form.

y = -3x + 5 Signup and view all the answers

Use a table of values to graph the function ƒ(x) = √x.

C. (1,1) (4,2) (9,3) Signup and view all the answers

Which function ƒ(x) is represented in the table of moped rental costs?

ƒ(x) = 0.5x + 10 Signup and view all the answers

What expression is equivalent to 3(x - 6) + 5(x - 4)?

8x - 38 Signup and view all the answers

Select the correct graph for the function ƒ(x) = -x - 7.

A Signup and view all the answers

How much would a customer pay to rent a golf cart for 4 hours?

$73 Signup and view all the answers

Which expression is equivalent to 9x - 3y - 5x + 7y + x + y?

5x + 5y Signup and view all the answers

Select the correct graph for the function ƒ(x) = the cube root of x.

A. (1,-2) (4,-4) (9,-6) Signup and view all the answers

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.

ƒ(x) = the cube root of (x + 8) - 3 Signup and view all the answers

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.