Review of Ch 6: Radical Equations and Inequalities

Front

What is a radical equation?

Back

An equation that contains a variable within a radical (square root, cube root, etc.).

Front

How do you solve a radical equation?

Back

Isolate the radical on one side, square both sides to eliminate the radical, and then solve the resulting equation.

Front

What is the principle of squaring both sides of an equation?

Back

If a = b, then a² = b². This is used to eliminate radicals but can introduce extraneous solutions.

Front

What is an extraneous solution?

Back

A solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

What is the difference between a radical equation and a radical inequality?

Back

A radical equation has an equal sign, while a radical inequality involves inequalities (>, <, ≥, ≤).

Front

How do you graph a radical function?

Back

Identify the domain, plot key points, and determine the end behavior based on the type of radical.

Front

What is the domain of the function f(x) = √(x - 2)?

Back

x must be greater than or equal to 2, so the domain is [2, ∞).

Front

What is the range of the function f(x) = √(x - 2)?

Back

The range is y ≥ 0, since the square root function outputs non-negative values.

Front

How do you simplify the expression (a + √b)(a - √b)?

Back

Use the difference of squares formula: a² - b.

Front

What is the formula for the sum of two functions f(x) and g(x)?

Back

(f + g)(x) = f(x) + g(x).