How does the equation $$y = \text{sqrt}(x)$$ transform when you add a constant to it?

Adding a constant shifts the graph vertically. For example, $$y = \text{sqrt}(x) + 2$$ shifts the graph up by 2 units.

What is the transformation represented by the equation $$y = \text{sqrt}(x - 4) - 2$$ ?

This equation shifts the graph of $$y = \text{sqrt}(x)$$ right by 4 units and down by 2 units.

What is the domain of the function $$y = \text{sqrt}(x - 1)$$ ?

The domain is the set of all x-values for which the function is defined. For this function, the domain is $$[1, \text{∞})$$ .

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

The range is the set of all possible output values. For this function, the range is $$[0, \text{∞})$$ .

What does the transformation 'reflect over the y-axis' mean for the function $$y = \text{sqrt}(x)$$ ?

Reflecting over the y-axis changes the function to $$y = \text{sqrt}(-x)$$ , which is not defined for positive x-values.

What is the effect of multiplying a radical function by a negative number?

Multiplying by a negative number reflects the graph over the x-axis. For example, $$y = -\text{sqrt}(x)$$ reflects the graph of $$y = \text{sqrt}(x)$$ .

How do you determine the vertical shift of a radical function?

The vertical shift is determined by the constant added or subtracted outside the radical. For example, in $$y = \text{sqrt}(x) + 3$$ , the graph shifts up by 3.

What is the significance of the value inside the radical?

The value inside the radical affects the horizontal shift of the graph. For example, $$y = \text{sqrt}(x - 2)$$ shifts the graph right by 2 units.

What is the general form of a radical function?

The general form of a radical function is $$y = a\text{sqrt}(x - h) + k$$ , where (h, k) is the vertex.

How does the graph of $$y = \text{sqrt}(x)$$ change when you replace x with (x - 3)?

Replacing x with (x - 3) shifts the graph to the right by 3 units, resulting in the function $$y = \text{sqrt}(x - 3)$$ .

A2 12.11 Radical Transformations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a radical function?

Back

2.

FLASHCARD QUESTION

Front

What does the graph of a square root function look like?

Back

The graph of a square root function is a curve that starts at a point on the x-axis (the vertex) and rises to the right, typically in the first quadrant.

Tags

CCSS.HSF-IF.C.7B

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7B

4.

FLASHCARD QUESTION

Front

What effect does a negative sign in front of a radical function have?

Back

Tags

CCSS.HSF-IF.C.7B

5.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSF-IF.C.7B

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.BF.B.3

7.

FLASHCARD QUESTION

Front

How do you identify the vertex of a radical function?

Back

Tags

CCSS.HSF-IF.C.7B

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