Cumulative Final Exam Review (edited fall 2024)

Front

What are vertical asymptotes and how are they determined?

Back

Vertical asymptotes are lines that a graph approaches but never touches. They are determined by the values of x that make the denominator of a rational function equal to zero.

Front

What is the value of sec(3π/2)?

Back

The value of sec(3π/2) is undefined because cos(3π/2) = 0, and sec is the reciprocal of cosine.

Front

How do you find the value of a function at a specific point, such as f(-8)?

Back

To find f(-8), substitute -8 into the function's equation and simplify to get the output value.

Front

What is the process for dividing rational expressions?

Back

To divide rational expressions, multiply by the reciprocal of the second expression and simplify.

Front

What is the value of cot(3π/4)?

Back

The value of cot(3π/4) is -1, as cotangent is the reciprocal of tangent.

Front

Define horizontal asymptotes and their significance in graphing functions.

Back

Horizontal asymptotes indicate the behavior of a function as x approaches infinity or negative infinity. They help determine the end behavior of the graph.

Front

What is the relationship between the degree of the numerator and denominator in determining horizontal asymptotes?

Back

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. If they are equal, the asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

Front

Explain the concept of end behavior in functions.

Back

End behavior describes how a function behaves as x approaches positive or negative infinity, often determined by the leading term of the polynomial.

Front

What is the significance of undefined values in trigonometric functions?

Back

Undefined values in trigonometric functions occur when the function's denominator is zero, indicating points where the function does not exist.

Front

How do you simplify a rational expression?

Back

To simplify a rational expression, factor both the numerator and denominator and cancel out any common factors.