Solving Square Root Functions Worksheet | Worksheets@TutorVista.com

Find the domain and the range of

y

x

\sqrt{8 x}

	a.		Both domain and range are all negative real numbers.
	b.		Both domain and range are all non-negative real numbers.
	c.		Domain: all real numbers greater than or equal to 8; range: all non-negative real numbers.
	d.		Domain: all non-negative real numbers; range: all real numbers greater than or equal to 8.

Solution:

Find the values of x for which the function is defined.

The function x8x exists only for 8x ≥ 0 ⇒ x ≥ 0.

The domain is the set of all non-negative real numbers.

The range of the function is the set of all non-negative real numbers.

Which of the following functions best represents the graph?

	a.		$y$ = $\sqrt{x}$ + 7
	b.		$y$ = $\sqrt{2 x + 5}$
	c.		$y$ = $\sqrt{2 x}$ + 1
	d.		$y$ = $\sqrt{x + 7}$

Solution:

On the graph, (2, 3) and (- 3, 2) points are marked. So, the function representing the graph should satisfy these two points.

Consider the function y = x + 7, if x = 2 then y = 8.414. So, this is not the required function.

Consider the function y = 2x + 5, if x = 2, then y = 3 and when x = - 3, then y is undefined. So, this is not the required function.

Consider the function y = 2x + 1, if x = 2, then y = 3 and when x = - 3, then y is undefined. So, this is not the required function.

Consider the function y = x + 7, if x = 2, then y = 3 and when x = - 3, then y = 2. So, this is the required function.

Which of the following functions best represents the graph?

	a.		$\frac{\sqrt{x} - 2}{x}$
	b.		$\sqrt{x - 4}$
	c.		$\frac{\sqrt{x - 4}}{x}$
	d.		$\sqrt{4 x}$ - 1

Solution:

The two points on the graph (1, - 1) and (4, 0) satisfy the funciton x - 2x.

The period T in seconds and the length L in inches of the pendulum are related as T = 2

π

\sqrt{\frac{L}{384}}

. Find the length of the pendulum in inches with period of 6 seconds.

	a.		350.17
	b.		102.76
	c.		580.64
	d.		298.32

Solution:

T = 2πL384

T² = (2π)2L384
[Square on both sides.]

384 · T² = (2π)2L
[Multiply both sides with 384.]

L = T2⋅384(2π)2
[Divide both sides by (2π )².]

L = (6)2⋅384(2π)2
[Substitute 6 for T.]

L = 350.17 inches.

The length of the pendulum = 350.17 inches.

10.

Find the lateral surface area

s

of a cone whose base radius

r

is 3 cm and height

h

is 4 cm.
Use the formula

s

π

r

\sqrt{r^{2} + h^{2}}

	a.		5 $π$ sq.cm.
	b.		15 $π$ sq.cm.
	c.		8 $π$ sq.cm.
	d.		24 $π$ sq.cm.

	a.		5 $\sqrt{3}$
	b.		2 $\sqrt{5}$
	c.		3 $\sqrt{7}$
	d.		8 $\sqrt{3}$

	a.		3 $\sqrt{2}$
	b.		5 $\sqrt{6}$
	c.		9 $\sqrt{2}$
	d.		2 $\sqrt{3}$

	a.		4 $\sqrt{3}$
	b.		3 $\sqrt{2}$
	c.		2 $\sqrt{3}$
	d.		3 $\sqrt{4}$

	a.		3 $\sqrt{6}$
	b.		5 $\sqrt{3}$
	c.		2 $\sqrt{6}$
	d.		6 $\sqrt{2}$