How do you determine the domain of a square root function like $$f(x) = \sqrt{x - 1}$$ ?

To determine the domain, set the expression inside the square root greater than or equal to zero: $$x - 1 \ge 0$$ . Solving this gives $$x \ge 1$$ .

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

The domain is found by setting the expression inside the square root non-negative: $$x + 3 \ge 0$$ , which gives $$x \ge -3$$ .

What is the range of the function $$f(x) = \sqrt{x} - 2$$ ?

The range is found by considering the minimum value of the function. Since $$\sqrt{x} \ge 0$$ , the minimum value of $$f(x)$$ is -2, so the range is $$y \ge -2$$ .

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

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

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

To find the domain, set the expression inside the square root non-negative: $$2 - x \ge 0$$ , which gives $$x \le 2$$ .

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

The range is all real numbers less than or equal to 0, expressed as $$y \le 0$$ .

How do you find the vertex of a square root function in the form $$f(x) = a\sqrt{x - h} + k$$ ?

The vertex of the function is the point (h, k). This is the point where the graph starts.

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

A negative 'a' reflects the graph over the x-axis, changing the function to $$f(x) = -a\sqrt{x - h} + k$$ .

How do you express the domain of a square root function that starts at a point other than zero?

The domain can be expressed in interval notation. For example, if the function starts at x = 1, the domain is written as $$[1, \infty)$$ .

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

What is the RANGE of a square root function?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

What is the general form of a square root function?

Back

7.

FLASHCARD QUESTION

Front

How does the value of 'a' affect the graph of a square root function?

Back

The value of 'a' affects the vertical stretch or compression of the graph. If |a| > 1, the graph is stretched; if 0 < |a| < 1, it is compressed.

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