Find the domain of the function: $$f(x)=\frac{x-1}{x^2-25}$$

The domain is $$(-\infty, -5) \cup (-5, 5) \cup (5, \infty)$$ . The function is undefined where the denominator is zero, i.e., at $$x = -5$$ and $$x = 5$$ .

Evaluate: $$\log_8\left(\frac{1}{64}\right)$$

The answer is $$-2$$ . This is because $$\frac{1}{64} = 8^{-2}$$ .

Simplify: $$e^{\ln(0.2)}$$

The answer is $$0.2$$ . The exponential function and the natural logarithm are inverse functions.

Evaluate: $$\ln\left(\frac{1}{\sqrt[]{e^7}}\right)$$

The answer is $$-\frac{7}{2}$$ . This can be simplified using properties of logarithms.

Find the horizontal asymptote of: $$f(x)=\frac{7x^2+8}{7x^2-8}$$

The horizontal asymptote is $$y = 1$$ . This is determined by the leading coefficients of the numerator and denominator.

State the properties of logarithms.

1. $$\log_b(mn) = \log_b(m) + \log_b(n)$$ (Product Property) 2. $$\log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n)$$ (Quotient Property) 3. $$\log_b(m^p) = p \cdot \log_b(m)$$ (Power Property) 4. $$\log_b(b) = 1$$ and $$\log_b(1) = 0$$ .

What is an asymptote?

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

How do you find vertical asymptotes?

Vertical asymptotes occur where the function is undefined, typically where the denominator equals zero.

What is the natural logarithm?

The natural logarithm, denoted as $$\ln(x)$$ , is the logarithm to the base $$e$$ , where $$e$$ is approximately equal to 2.718.

Evaluate: $$\ln(e^3)$$

The answer is $$3$$ . This follows from the property of logarithms that states $$\ln(e^x) = x$$ .

What is the relationship between exponential and logarithmic functions?

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

Define a rational function.

A rational function is a function that can be expressed as the quotient of two polynomials.

What is the significance of the leading coefficient in polynomial functions?

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

Precalc. AB Semester Final Part 1 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

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2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

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CCSS.HSF.BF.B.5

4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

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CCSS.HSF-IF.C.7D

6.

FLASHCARD QUESTION

Front

Define the domain of a function.

Back

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

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

7.

FLASHCARD QUESTION

Front

What is a logarithm?

Back

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

Tags

CCSS.HSF.BF.B.5

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