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# Algebra 2B End of Semester Test

Created by
@PromisingStonehenge

## Questions and Answers

5(2)^x = 1,280

### Match each series with the equivalent series written in sigma notation:

<p>3 + 12 + 48 + 192 + 768 = 3(4) 4 + 32 + 256 + 2,048 + 16,384 = 4(8) 2 + 6 + 18 + 54 + 162 = 2(3) 3 + 15 + 75 + 375 + 1,875 = 3(5)</p> Signup and view all the answers

### What does the function h(x) look like?

<p>h(x) = {-6, -9 for -4 &lt; x &lt; -3, 1 for -2 &lt; x &lt; 2, 4 for 2 &lt; x &lt; 8}</p> Signup and view all the answers

### Function g is continuous.

<p>True</p> Signup and view all the answers

### What should Ronald do with the functions regarding the height of the chest?

<p>Multiply functions + sqrt(x)</p> Signup and view all the answers

### Which expression is equal to f(x) * g(x)?

<p>x-2/x+6</p> Signup and view all the answers

### As x approaches positive infinity, f(x) approaches ___ and g(x) approaches ___.

<p>[positive infinity] and [negative infinity]</p> Signup and view all the answers

### What did Jane record about her marigold sapling?

<p>The function is increasing, but the average rate of change is decreasing.</p> Signup and view all the answers

### What is the approximate value for the solution to the equation f(x) = g(x)?

<p>7/8</p> Signup and view all the answers

### Using a table of values, what is the approximate solution to the equation f(x) = g(x) to the nearest quarter of a unit?

<p>x ≈ -2.25</p> Signup and view all the answers

### Logarithmic Expressions

• Equivalent expressions: log10(20x^5) - 1 simplifies to log10(10x).

### Logarithmic Equations and Their Values

• Corresponding values for logarithmic equations:
• log5x=4 → x = 625
• log4x=2 → x = 16
• log10x=3 → x = 1,000
• log2x=5 → x = 32

### Solving Equations

• Solve 1.5(4)^2x = 12 to find x ≈ 0.75.
• Approximate solution for 4Inx - 8 = 12: x ≈ 148.4.

### Transformations of Exponential Functions

• Transformed function g(x) = 3f(x) where f(x) is the parent exponential function f(x) = e^x.
• For g(x) = -2f(x) + 1 derived from f(x) = 10^x, the range is (-∞, 1).

### Characteristics of Function Graphs

• Function f has a range of all real numbers and decreases as x approaches 0.
• Transformations of f(x) = ln x provide varying features, such as vertical asymptote and intercept changes.

### Sequence Representation

• Explicit form of the sequence 16, 24, 36, 54 is f(n) = 16(3/2)^(n - 1).

### Planning and Profit Analysis

• Natalie drives approximately 900 miles each month, starting at 800 miles.
• Jessica's five-year total profit calculation remains unclear, initially posing a profit of \$3,125 in the first year.

### Sigma Notation

• Conversions to sigma notation for series:
• 3 + 12 + 48 + 192 + 768 → 3(4)
• 4 + 32 + 256 + 2,048 + 16,384 → 4(8)

### Graphical Transformations and Functions

• Midline for function y = 1/2cos(2x) - 1 is at y = -1.
• Graph transformations include shifts and frequency adjustments.

### Angles and Trigonometry

• Angle 0 = 7x/4 gives tan(0) = -1, with the reference angle being 45°.
• For cos(0) = -3/10 in quadrant II, tan(0) value equals -√91/3.

### Probability and Statistics

• Function g exhibits continuity, with limits approaching positive infinity as x increases.
• A factory's tire molding machine has a 0.2% failure rate, with actual faults at a 0.4% difference from theoretical.

### Sampling and Confidence Intervals

• A sample of 1,000 students reveals a 59% preference for coffee; the population proportion may differ.
• The city council mandates at least 18 trees per block, averaging 21.3 trees, ensuring environmental standards.

### Effectiveness of Products

• Analysis concludes Fabric B as more durable than Fabric A based on double rub ratings, affirming its medium-duty classification.

### Experimental Studies

• Thad conducted an experiment to compare window cleaners by washing half the windows with each brand, demonstrating a practical study approach.

### Growth Measurement in Gardening

• Jane's marigold sapling grows at an increasing rate with decreasing average change over time.

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## Description

This quiz includes practice flashcards for Ms. Walker's Algebra 2B class. It focuses on exponential growth and solving equations related to a fundraising scenario. Test your understanding of functions and their applications in real-world problems.

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