Algebra II Trig Placement Test Review

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Questions and Answers

What is the result of factoring $10x^2 - 7x - 3$?

  • (2x + 3)(5x - 1)
  • (5x + 1)(2x - 3)
  • (10x - 3)(x + 1)
  • (10x + 3)(x - 1) (correct)

What is the domain of the function?

{-2, 0, 2}

What defines a function?

Each x value goes to only one y value.

What is a parabola?

<p>A shape where the extreme point (max or min) is the vertex, and zeros are the x-intercepts.</p> Signup and view all the answers

What does f(x) represent?

<p>f(x) = y; f(2) is solved if x is 2.</p> Signup and view all the answers

True or False: Any number raised to the power of 1 is itself.

<p>True (A)</p> Signup and view all the answers

What is the product rule in exponents?

<p>Add the exponents when multiplying with the same base.</p> Signup and view all the answers

What is the power rule in exponents?

<p>Multiply the exponents when raising a power to a power.</p> Signup and view all the answers

What is the quotient rule in exponents?

<p>Subtract the exponents when dividing with the same base.</p> Signup and view all the answers

True or False: Any non-zero number raised to the zero power is 0.

<p>False (B)</p> Signup and view all the answers

What do negative exponents represent?

<p>A nonzero number raised to a negative power equals its reciprocal raised to the opposite positive power.</p> Signup and view all the answers

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Study Notes

Factoring

  • The expression (10x^2 - 7x - 3) can be factored into ((10x + 3)(x - 1)).

Domain

  • The domain is a set of x-values, which in this case is ({-2, 0, 2}).

Functions

  • A function uniquely maps each x-value to a single y-value, exemplified by pairs like ((2, 3), (3, 4), (4, 2)).

Parabola

  • A parabola has a vertex that represents its extreme point (maximum or minimum), while the x-intercepts are known as zeros.

Function Notation

  • (f(x)) denotes a function with output (y), where (f(2)) requires solving for y when (x = 2).

Rule of One

  • Any number raised to the power of 1 remains unchanged, while 1 raised to any power results in 1.

Product Rule

  • When multiplying two expressions with the same base, their exponents can be added together.

Power Rule

  • When raising a power to another power, multiply the exponents.

Quotient Rule

  • Dividing two expressions with the same base entails subtracting the exponents while retaining the base.

Zero Exponent Rule

  • Any non-zero number raised to the zero power equals 1.

Negative Exponents

  • A nonzero number with a negative exponent equals the reciprocal of that number raised to the opposite positive exponent (e.g., (4^{-2} = \frac{1}{4^2})).

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