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Algebra 1 : How to find the domain of a function

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Example Questions

Example Question #31 : How To Find The Domain Of A Function

Which function has as its domain the set of all real numbers?

Possible Answers:

$f(x)= \sqrt{x^{2}- 64}$

$j(x)= \sqrt{x^{3}+ 64}$

None of the other choices gives a correct answer.

$g(x)= \sqrt{x^{2}+ 64}$

$h(x)= \sqrt{x^{3}-64}$

Correct answer:

$g(x)= \sqrt{x^{2}+ 64}$

Explanation:

The domain of a square root function is the set of all values of for which the radicand is nonnegative. Three of these functions are undefined for at least one value of , since this value yields a negative radicand.

is outside the domain of , , and by virtue of causing their radicands to be negative:

$f(x)= \sqrt{x^{2}- 64}$ :

$(-5)^{2}- 64 = 25- 64 = -39$

$h(x)= \sqrt{x^{3}-64}$

$(-5)^{3}- 64 =-125 - 64 = -189$

$j(x)= \sqrt{x^{3}+ 64}$

$(-5)^{3}+ 64 =-125 + 64 = -61$

We examine . We show that the radical can never be negative by setting it as such, and trying to solve for , as follows:

$x^{2}+ 64< 0$

$x^{2}< -64$

Since $x^{2}$ must be nonnegative, it is always greater than . Therefore, the inequality has no solution. Consequently, the radicand of is always nonnegative, and has the set of all real numbers as its domain.

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Example Question #132 : Algebraic Functions

Find the domain of y=x^2+8 .

Possible Answers:

[-8,8]

$(-\infty, 8)$

$[-8, \infty)$

$(-\infty, \infty)$

$(8, \infty)$

Correct answer:

$(-\infty, \infty)$

Explanation:

This function resembles a parabola since the highest order is within the term x^2 .

There are no denominators where the variable is undefined.

The domain refers to the existing x-values which lie on the graph.

This parabola will only shift upward eight units and will not affect the domain.

The answer is: $(-\infty, \infty)$

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Example Question #132 : Algebraic Functions

What is the domain of the following function:

x^2+x+10

Possible Answers:

$(-\infty, \infty)$

[0,10]

$[10, \infty)$

$[-\infty, \infty]$

$(-\infty,10]$

Correct answer:

$(-\infty, \infty)$

Explanation:

The easiest way to figure this out is by knowing that the domain of all quadratics without any restrictions is always all real numbers, though this problem can be solved graphically, too.

Either method is correct and your correct answer is:

$(-\infty, \infty)$

It is important, too, to note that soft brackets must be used when working with infinity.

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Example Question #34 : How To Find The Domain Of A Function

What is the domain of the following function:

$\frac{x+2}{x-2}=0$

Possible Answers:

None of the above

$(-\infty,-2]\cup[-2, \infty)$

$(-\infty,-2)\cup(-2, \infty)$

$(-\infty,2)\cup(2, \infty)$

$(-\infty,2]\cup[2, \infty)$

Correct answer:

$(-\infty,2)\cup(2, \infty)$

Explanation:

There are two important components of this problem. First we must set the denominator equal to zero and solve for . This gives us values that can't be because the denominator can never equal zero.

Doing this, we get x=2 , so, can be any number except for a positive two.

The other key to this problem is knowing the difference between brackets and parentheses. The square brackets mean that a number is included, whereas the parentheses mean that it is not. Because cannot equal 2, we need to use the parentheses.

This makes:

$(-\infty,2)\cup(2, \infty)$

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Example Question #181 : Functions And Lines

Determine the Range of the parabola as shown in figure d

Possible Answers:

$\left \{ y|-3\leq y< \infty \right \}$

$\left \{ y|-\infty < y< \infty \right \}$

$\left \{ y|-3\leq y< \infty or-\infty < y\leq -3 \right \}$

$\left \{ y|-\infty < y\leq -3 and -3\leq y< \infty \right \}$

$\left \{ y|-\infty < y\leq -3 \right \}$

Correct answer:

$\left \{ y|-\infty < y\leq -3 \right \}$

Explanation:

From the figure one can see the Range varies from to $-\infty$ .

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Algebra 1 : How to find the domain of a function

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #31 : How To Find The Domain Of A Function

Example Question #132 : Algebraic Functions

Example Question #132 : Algebraic Functions

Example Question #34 : How To Find The Domain Of A Function

Example Question #181 : Functions And Lines

All Algebra 1 Resources

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