What is the significance of the vertex in a square root function?

The vertex of a square root function is the point where the graph starts. For the parent function $$f(x) = \text{sqrt}(x)$$ , the vertex is at (0,0).

How do you determine the domain from a given square root function?

To determine the domain, set the expression inside the square root greater than or equal to zero and solve for x. For example, for $$f(x) = \text{sqrt}(x - 3)$$ , the domain is $$[3, \text{∞})$$ .

What is the relationship between the domain and range of square root functions?

For square root functions, the domain is the set of x-values that make the expression under the square root non-negative, while the range is the set of y-values that are non-negative.

What is the x-intercept of the function $$f(x) = \text{sqrt}(x - 4)$$ ?

To find the x-intercept, set $$f(x) = 0$$ . Thus, $$\text{sqrt}(x - 4) = 0$$ leads to $$x = 4$$ , so the x-intercept is (4,0).

What is the domain of the function $$f(x) = \text{sqrt}(x + 2)$$ ?

To find the domain, set the expression inside the square root non-negative: $$x + 2 \text{ ≥ } 0$$ . This gives $$x \text{ ≥ } -2$$ , so the domain is $$[-2, \text{∞})$$ .

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

The range of the function is all non-negative values since the square root function outputs values starting from 0. Therefore, the range is $$[0, \text{∞})$$ .

How do you graph a square root function?

To graph a square root function, identify the vertex, plot points by substituting x-values into the function, and connect the points smoothly, ensuring the graph only exists in the first quadrant.

What is the effect of a vertical stretch on a square root function?

A vertical stretch increases the steepness of the graph. For example, $$f(x) = 2\text{sqrt}(x)$$ stretches the graph vertically by a factor of 2.

Attributes of Square Root Functions Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the domain of a square root function?

Back

2.

FLASHCARD QUESTION

Front

What is the range of a square root function?

Back

3.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSF-IF.C.7B

4.

FLASHCARD QUESTION

Front

What is the parent function of square root functions?

Back

5.

FLASHCARD QUESTION

Front

What transformations can be applied to the square root function?

Back

Tags

CCSS.HSF.BF.B.3

6.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSF-IF.C.7B

7.

FLASHCARD QUESTION

Front

How does the value inside the square root affect the graph?

Back

Tags

CCSS.HSF-IF.C.7B

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