What is the domain of the function $$y = \text{sqrt}(x)$$ ?

The domain is $$[0, \text{infinity})$$ because the square root function is only defined for non-negative values.

What is the range of the function $$y = \text{sqrt}(x)$$ ?

The range is $$[0, \text{infinity})$$ because the output of the square root function is always non-negative.

How do you find the x-intercept of a radical function?

To find the x-intercept, set y = 0 and solve for x. For example, for $$y = \text{sqrt}(x)$$ , set $$0 = \text{sqrt}(x)$$ , which gives x = 0.

What is the equation for a cube root function?

The general form is $$y = \text{cbrt}(x - h) + k$$ , where (h, k) is the point of inflection.

What is the domain of the function $$y = \text{cbrt}(x)$$ ?

The domain is $$(-\text{infinity}, \text{infinity})$$ because cube roots are defined for all real numbers.

What is the range of the function $$y = \text{cbrt}(x)$$ ?

The range is $$(-\text{infinity}, \text{infinity})$$ because cube roots can produce all real numbers.

How does the graph of $$y = \text{cbrt}(x)$$ differ from $$y = \text{sqrt}(x)$$ ?

The graph of $$y = \text{cbrt}(x)$$ is symmetric about the origin and extends in both directions, while $$y = \text{sqrt}(x)$$ only extends to the right.

What is the effect of a negative sign in front of a radical function?

A negative sign in front of a radical function reflects the graph across the x-axis. For example, $$y = -\text{sqrt}(x)$$ reflects the graph of $$y = \text{sqrt}(x)$$ .

What is the importance of identifying the vertex in a radical function?

The vertex indicates the starting point of the graph and helps in understanding the transformations applied to the basic radical function.

Graphing Radical Equations Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

Tags

CCSS.HSA.REI.A.2

2.

FLASHCARD QUESTION

Front

What is the general form of a square root function?

Back

Tags

CCSS.HSF-IF.C.7B

3.

FLASHCARD QUESTION

Front

Back

The graph starts at the origin (0,0) and increases gradually to the right, forming a half-parabola.

Tags

CCSS.HSF-IF.C.7B

4.

FLASHCARD QUESTION

Front

What effect does adding a constant outside the radical have on the graph?

Back

Tags

CCSS.HSF-IF.C.7B

5.

FLASHCARD QUESTION

Front

What effect does subtracting a constant outside the radical have on the graph?

Back

Tags

CCSS.HSF-IF.C.7B

6.

FLASHCARD QUESTION

Front

What does it mean to shift a graph left or right?

Back

Tags

CCSS.HSF-IF.C.7B

7.

FLASHCARD QUESTION

Front

Back

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