What is the DOMAIN of the function $$f(x) = \\sqrt{x - 3}$$ ?

The domain is $$[3, \\infty)$$ because the expression inside the square root must be greater than or equal to zero.

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

The domain is $$(-\\infty, 0]$$ because the expression inside the square root must be non-negative.

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

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

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

A vertical shift moves the graph up or down. For example, $$f(x) = \\sqrt{x} + 2$$ shifts the graph up by 2 units.

What is the effect of a horizontal shift on the square root function?

A horizontal shift moves the graph left or right. For example, $$f(x) = \\sqrt{x - 3}$$ shifts the graph to the right by 3 units.

What happens to the graph of a square root function when it is reflected over the x-axis?

Reflecting the graph over the x-axis changes the function to $$f(x) = -\\sqrt{x}$$ , which inverts the output values.

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

A vertical stretch multiplies the output by a factor greater than 1. For example, $$f(x) = 2\\sqrt{x}$$ stretches the graph vertically by a factor of 2.

What is the effect of a horizontal compression on the square root function?

A horizontal compression multiplies the input by a factor greater than 1. For example, $$f(x) = \\sqrt{2x}$$ compresses the graph horizontally.

What is the inverse of the square root function?

The inverse of the square root function $$f(x) = \\sqrt{x}$$ is $$f^{-1}(x) = x^2$$ , defined for $$x \\ge 0$$ .

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

To find the x-intercept, set the function equal to zero and solve for x. For example, for $$f(x) = \\sqrt{x}$$ , the x-intercept is at $$x = 0$$ .

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

The vertex is the point where the graph starts, typically at the lowest point for the standard square root function, which is at (0,0).

Attributes of Square Root Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the DOMAIN of a square root function?

Back

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

This is a square root function.

5.

FLASHCARD QUESTION

Front

What is the parent function of square root functions?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

How does the graph of a square root function behave as x increases?

Back

As x increases, the value of the square root function also increases, but at a decreasing rate.

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