Precalculus Midterm

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a. It indicates a point of discontinuity in the function.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b where a function approaches the value b as x approaches infinity or negative infinity. It describes the end behavior of the function.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the x and y variables in the equation and solve for y. The resulting equation is the inverse function.

Front

What is the transformation of a function?

Back

A transformation of a function involves changing its position, size, or orientation. Common transformations include translations, reflections, stretches, and compressions.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph. Formally, a function f(x) is continuous at a point x = a if lim (x -> a) f(x) = f(a).

Front

What is a point of discontinuity?

Back

A point of discontinuity is a point at which a function is not continuous. This can occur due to a hole, vertical asymptote, or jump in the function.

Front

How do you solve an equation involving a square root?

Back

To solve an equation involving a square root, isolate the square root on one side, square both sides of the equation, and then solve for the variable. Check for extraneous solutions.

Front

What is cross-multiplication?

Back

Cross-multiplication is a method used to solve equations involving fractions. For an equation of the form \( \frac{a}{b} = \frac{c}{d} \), cross-multiplication gives \( a \cdot d = b \cdot c \).

Front

What is the absolute value function?

Back

The absolute value function, denoted as |x|, returns the non-negative value of x. It is defined as |x| = x if x >= 0 and |x| = -x if x < 0.

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. It can be restricted by factors like square roots or denominators.