A2AC Unit 2B Review

Front

What is cross multiplication?

Back

Cross multiplication is a method used to solve proportions. If you have a proportion of the form \( \frac{a}{b} = \frac{c}{d} \), you can cross multiply to get \( a \cdot d = b \cdot c \).

Front

Solve the proportion: \( \frac{x}{2x+7} = \frac{x-5}{x-1} \)

Back

Cross multiplying gives: \( x(x-1) = (2x+7)(x-5) \). The solutions are \( x = -5 \) and \( x = 7 \).

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, \( \frac{a}{b} = \frac{c}{d} \).

Front

Select the solution(s) to the proportion: \( \frac{x+3}{x-1} = \frac{5x}{2} \)

Back

The solutions are \( -\frac{3}{5} \) and \( 2 \).

Front

What is an identity in mathematics?

Back

An identity is an equation that is true for all values of the variable. For example, \( x + 0 = x \) is an identity.

Front

What are asymptotes?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical, horizontal, or oblique.

Front

Find the asymptotes for the function: \( \frac{1}{x+3} \)

Back

The vertical asymptote is at \( x = -3 \) and the horizontal asymptote is at \( y = 0 \).

Front

What is the difference between a vertical and horizontal asymptote?

Back

A vertical asymptote occurs where the function approaches infinity, while a horizontal asymptote describes the behavior of the function as \( x \) approaches infinity.

Front

How do you determine if an equation is an identity?

Back

To determine if an equation is an identity, simplify both sides of the equation. If they are equal for all values of the variable, it is an identity.

Front

What is the solution to the equation \( 2x + 3 = 7 \)?

Back

The solution is \( x = 2 \).