Exam Review

Front

What is end behavior in functions?

Back

End behavior describes the behavior of a function as the input values approach positive or negative infinity.

Front

What is the correct end behavior for the function as \( x \rightarrow \infty \)?

Back

The correct end behavior is \( f(x) \rightarrow \infty \).

Front

How can you determine if a function is even, odd, or neither?

Back

A function is even if \( f(-x) = f(x) \), odd if \( f(-x) = -f(x) \), and neither if it does not satisfy either condition.

Front

What is the definition of a slant asymptote?

Back

A slant asymptote is a diagonal line that a function approaches as \( x \) approaches infinity or negative infinity.

Front

How do you find the slant asymptote of a rational function?

Back

Perform polynomial long division on the numerator by the denominator.

Front

What is 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.

Front

How do you find the domain of a function?

Back

Identify any restrictions on the variable, such as division by zero or square roots of negative numbers.

Front

What is the logarithmic identity used to simplify logarithmic expressions?

Back

The identity is \( \log_b(m) - \log_b(n) = \log_b\left(\frac{m}{n}\right) \).

Front

What is the solution to the equation \( \log_5y - \log_58 = \log_51 \)?

Back

The solution is \( y = 8 \).

Front

What does it mean for a function to be 'even'?

Back

A function is even if its graph is symmetric with respect to the y-axis.