Precalc. AB Semester Final Part 1

Front

What is the definition of an asymptote?

Back

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

Front

What is the logarithmic identity for condensing logarithms?

Back

The identity states that \( a \log_b(c) = \log_b(c^a) \) and \( \log_b(c) - \log_b(d) = \log_b(\frac{c}{d}) \).

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor of the form \( x - c \).

Front

What is the relationship between exponential and logarithmic functions?

Back

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

Front

What is the value of \( e^{\ln(a)} \)?

Back

The value of \( e^{\ln(a)} \) is \( a \) for any positive number \( a \).

Front

How do you evaluate \( \log_b(a) \)?

Back

To evaluate \( \log_b(a) \), find the exponent \( x \) such that \( b^x = a \).

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that \( \log_b(a) = \frac{\log_k(a)}{\log_k(b)} \) for any positive base \( k \).

Front

What is the definition of a polynomial function?

Back

A polynomial function is a function that can be expressed in the form \( f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 \), where \( a_n, a_{n-1}, ..., a_0 \) are constants and \( n \) is a non-negative integer.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that \( \log_b(\frac{a}{c}) = \log_b(a) - \log_b(c) \).