Precalculus Fall 2024 Final

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates values that the function cannot take.

Front

How do you find the zeros of a rational function?

Back

To find the zeros of a rational function, set the numerator equal to zero and solve for x. The zeros are the x-values where the function crosses the x-axis.

Front

What is the initial value in an exponential function of the form y = ab^x?

Back

The initial value is the value of y when x = 0, which is equal to a.

Front

What characterizes an even function?

Back

An even function satisfies the property f(-x) = f(x) for all x in its domain, meaning its graph is symmetric about the y-axis.

Front

How do you calculate the average rate of change of a function?

Back

The average rate of change of a function between two points (x1, y1) and (x2, y2) is given by the formula (y2 - y1) / (x2 - x1).

Front

What is the significance of the horizontal asymptote in a rational function?

Back

A horizontal asymptote indicates the behavior of a function as x approaches infinity or negative infinity, showing the value that the function approaches.

Front

What is the difference between a removable and non-removable discontinuity?

Back

A removable discontinuity occurs when a factor cancels in the numerator and denominator, while a non-removable discontinuity occurs when the function approaches infinity at a certain x-value.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the leading term. If the leading coefficient is positive, the function rises to the right; if negative, it falls to the right.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have at most n real zeros, according to the Fundamental Theorem of Algebra.

Front

What is the formula for the vertex of a parabola in standard form?

Back

For a parabola in the form y = ax^2 + bx + c, the vertex can be found using the formula (-b/(2a), f(-b/(2a))).