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Algebra II: Exponential, Logarithmic, and Trigonometric Functions

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How are exponential and logarithmic functions related, and how do you use the properties of logarithms?

Understand the inverse relationship between exponential and logarithmic functions; convert between exponential and logarithmic form; apply the product, quotient, and power properties of logarithms; and use the natural base e and natural logarithm.
A NY Regents Algebra II answer on exponential and logarithmic functions: the inverse relationship, converting between forms, the product/quotient/power log properties, and the natural base e and natural log.
9 min answer →

How do amplitude, period, midline, and phase shift shape the graph of a sine or cosine function?

Identify the amplitude, period, midline, and phase shift of a sinusoidal function from its equation; graph sine and cosine functions; and build a sinusoidal model of a periodic real-world situation.
A NY Regents Algebra II answer on sinusoidal functions: reading amplitude, period, midline, and phase shift from the equation, graphing sine and cosine, and modeling periodic phenomena such as tides and temperature.
9 min answer →

How does radian measure work, and how does the unit circle extend the trig functions to any angle?

Convert between degrees and radians; use the unit circle to define the sine and cosine of any angle as coordinates of a point; evaluate the trig functions at special angles; and apply the Pythagorean identity.
A NY Regents Algebra II answer on radian measure and the unit circle: converting degrees and radians, sine and cosine as unit-circle coordinates, special-angle values, reference angles, and the Pythagorean identity.
9 min answer →

How do arithmetic and geometric sequences work, and how do you sum a series?

Write explicit and recursive formulas for arithmetic and geometric sequences; find a specified term; use sigma notation; and apply the arithmetic and finite geometric series sum formulas.
A NY Regents Algebra II answer on sequences and series: explicit and recursive formulas for arithmetic and geometric sequences, finding a term, sigma notation, and the arithmetic and finite geometric series sums.
9 min answer →

How do you solve exponential and logarithmic equations, and how do you model growth and decay?

Solve exponential equations (matching bases or taking logarithms) and logarithmic equations (condensing then rewriting in exponential form), check for extraneous solutions, and model exponential growth, decay, and compound interest.
A NY Regents Algebra II answer on solving exponential and logarithmic equations: matching bases, taking logs, condensing and rewriting logs, extraneous solutions, and modeling growth, decay, and compound interest.
10 min answer →