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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-BF.B.4A

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.

Tags

CCSS.HSF.BF.B.3

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.

Tags

CCSS.HSA.REI.A.2

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 \( a \cdot d = b \cdot c \).

Tags

CCSS.6.EE.B.7

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.

Tags

CCSS.HSF-IF.C.7D

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.