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Algebra 2 Exam Review
Simplifying and Multiplying Rational Expressions
The lecture begins with a review of simplifying rational expressions by canceling common factors after factoring. It emphasizes the importance of factoring first. The discussion then moves to multiplying fractions, highl
Dividing Rational Expressions and Finding Common Denominators
The lecture continues with dividing fractions, reminding students to "keep, change, flip" (multiply by the reciprocal). Factoring is again emphasized as part of the process. The speaker demonstrates canceling common fact
Subtracting Rational Expressions with Missing Factors
The lecture explains how to subtract rational expressions by introducing missing factors to achieve a common denominator. It emphasizes the importance of distributing negative signs correctly when subtracting numerators.
Solving Rational Equations and Extraneous Solutions
The lecture shifts to solving rational equations. The strategy involves obtaining a common denominator, discarding it, and solving the resulting numerator equation. The concept of extraneous solutions is introduced, emph
Vertical and Horizontal Asymptotes
The lecture explains how to find vertical and horizontal asymptotes of rational functions. Vertical asymptotes occur where the denominator equals zero, creating a problem in the domain. The speaker notes that if the same
Composite Functions
The lecture covers composite functions, where one function is placed inside another. The notation F of G is explained, demonstrating how to substitute the G function into the F function. The reverse, G of F, is also show
Finding and Verifying Inverse Functions
The lecture explains how to find the inverse of a function by switching the x and y variables and then solving for y. The proper notation for inverse functions is introduced. To verify that two functions are inverses, yo
Exponential Growth and Decay
This section briefly discusses exponential growth and decay. The key factor in determining growth or decay is the base of the exponential function. If the base is greater than one, it represents growth; if it's a decimal
Condensing and Expanding Logarithms
The lecture reviews the properties of logarithms for condensing and expanding logarithmic expressions. Multiplication inside a logarithm becomes addition outside, division becomes subtraction, and exponents can be moved
Solving Logarithmic Equations and Exponential Growth/Decay Applications
The lecture continues with solving logarithmic equations by converting them to exponential form. The base of the logarithm becomes the base of the exponential, and the logarithm's answer becomes the exponent. The lecture
Compound Interest and Midpoint/Distance Formulas
The lecture covers compound interest, explaining the formula and the meaning of 'n' for different compounding periods (quarterly, daily, semiannually, weekly). It then transitions to the midpoint and distance formulas. T
Conics: Circles and Ellipses
The lecture begins the conics section with the equation of a circle, including cases with a center (h, k). It then moves to ellipses, explaining how to write the equation of an ellipse given its center, vertex, and focus
Conics: Finding Foci of Ellipses and Introduction to Parabolas
The lecture continues with ellipses, demonstrating how to find the coordinates of the foci. The formula relating a, b, and c is used again. The lecture then introduces parabolas, correcting a mistake in the example probl
Conics: Hyperbolas and Asymptotes
The lecture concludes with hyperbolas, distinguishing them from parabolas. The key difference is the minus sign in the equation. The larger number is identified as a squared, and the smaller number as b squared. The lect
