Expand $$\log_6\left(\frac{x^3}{yz}\right)$$

$$3\log_6x - \log_6y - \log_6z$$

Identify the end behavior of the function $$h(x) = -1x^4 - 3x^3 + 3$$

The end behavior is determined by the leading term, which is negative, indicating that as $$x \to \infty$$ , $$h(x) \to -\infty$$ and as $$x \to -\infty$$ , $$h(x) \to -\infty$$ .

Determine the domain of the function $$f(x) = \frac{1}{x^2 - 4}$$

The domain is $$(-\infty, -4) \cup (-4, 4) \cup (4, \infty)$$ .

State the power property of logarithms.

$$\log_b(m^p) = p \cdot \log_b(m)$$ .

What is the definition of a composite function?

A composite function $$g(f(x))$$ is formed by applying function $$g$$ to the result of function $$f$$ .

What is the leading coefficient test for polynomial functions?

The leading coefficient test helps determine the end behavior of a polynomial function based on the sign and degree of the leading term.

What is the definition of the domain of a function?

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

What is the definition of a logarithm?

A logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base be raised to produce a given number.

What is the relationship between exponential and logarithmic functions?

Exponential functions and logarithmic functions are inverses of each other; if $$y = b^x$$ , then $$x = \log_b(y)$$ .

What is the significance of the leading term in a polynomial function?

The leading term determines the end behavior of the polynomial function as $$x$$ approaches infinity or negative infinity.

What is the difference between a rational function and a polynomial function?

A rational function is a ratio of two polynomials, while a polynomial function is a sum of terms with non-negative integer exponents.

Precalc. BC Semester 1 Exam Practice

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Mathematics

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12th Grade

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Hard

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CCSS

HSF-BF.A.1C, HSF.BF.B.5, 8.F.A.1

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