What is the significance of the square root in solving equations?

Square roots can introduce extraneous solutions, so solutions must be checked in the original equation.

What is the effect of adding a constant to a square root function?

Adding a constant shifts the graph vertically. For example, $$y = \\sqrt{x} + 5$$ shifts the graph up by 5.

How do you determine the domain of a square root function?

Set the expression inside the square root greater than or equal to zero.

What is an extraneous solution?

An extraneous solution is a solution that does not satisfy the original equation.

How do you check if a solution is valid for a square root equation?

Substitute the solution back into the original equation to verify.

What is the relationship between the domain and range of the function $$y = \\sqrt{x} + 5$$ ?

The domain is all non-negative x-values, and the range is all y-values starting from 5 and above.

Solving Square Root Equations Flashcards: 15 Cards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the domain of the function $y = \sqrt{x} + 5$ ?

Back

Domain: $x \ge 0$ .

2.

FLASHCARD QUESTION

Front

What is the range of the function $y = \sqrt{x} + 5$ ?

Back

Range: $y \ge 5$ .

3.

FLASHCARD QUESTION

Front

Solve the equation $(x + 2)^{\frac{1}{2}} + 3 = 7$ .

Back

x = 14.

4.

FLASHCARD QUESTION

Front

What is the parent function of the square root function?

Back

Parent function: $y = \sqrt{x}$ .

5.

FLASHCARD QUESTION

Front

Find the domain of the function $y = \sqrt{3x - 11}$ .

Back

Domain: $x \ge \frac{11}{3}$ .

6.

FLASHCARD QUESTION

Front

Find the range of the function $y = \sqrt{3x - 11}$ .

Back

Range: $y \ge 0$ .

7.

FLASHCARD QUESTION

Front

Solve the equation $\sqrt{3x - 11} = \sqrt{5 - x}$ .

Back

x = 4.

8.

FLASHCARD QUESTION

Front

What is the definition of a square root?

Back

A square root of a number $a$ is a number $b$ such that $b^2 = a$ .

9.

FLASHCARD QUESTION

Front

What is the graphical representation of the function $y = \sqrt{x}$ ?

Back

The graph starts at the origin (0,0) and increases gradually to the right.

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