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Algebra II : Functions and Graphs

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Example Questions

Example Question #51 : Introduction To Functions

Squareroot

$\textup{What is the domain of }y=\sqrt{x}\textup{ ?}$

Possible Answers:

x>0

$x= all \:real \: numbers$

$x\geq0$

$y \neq0$

Correct answer:

$x\geq0$

Explanation:

You cannot take the square root of a negative number.

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Example Question #52 : Introduction To Functions

Identity

$\textup{What is the domain of y = x ?}$

Possible Answers:

$y= all \:real \: numbers$

y>0

$x\geq0$

$y\neq0$

Correct answer:

$y= all \:real \: numbers$

Explanation:

The function includes all possible y-values (outputs). There is nothing you can put in for y that won't work.

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Example Question #53 : Introduction To Functions

Parabola

$\textup{What is the range of }y=x^{2}\textup{ ?}$

Possible Answers:

y>0

$y= all \:real \: numbers$

$y\geq0$

x>0

Correct answer:

$y\geq0$

Explanation:

Squaring an input cannot produce a negative output.

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Example Question #54 : Introduction To Functions

Cubing

$\textup{What is the range of }y=x^{3}\textup{ ?}$

Possible Answers:

$y\leq1$

y>0

$x= all \:real \: numbers$

$y= all \:real \: numbers$

Correct answer:

$y= all \:real \: numbers$

Explanation:

The function includes all possible y-values (outputs). There is nothing you can put in for y that won't work.

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Example Question #55 : Introduction To Functions

Exponential

$\textup{What is the range of }y=2^{x}\textup{?}$

Possible Answers:

$y\geq0$

y>0

$y= all \:real \: numbers$

$x\geq0$

Correct answer:

y>0

Explanation:

A number taken to a power must be positive.

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Example Question #56 : Introduction To Functions

Squareroot

$\textup{What is the range of } y=\sqrt{x}\textup{ ?}$

Possible Answers:

$y= all \:real \: numbers$

$y\geq0$

y>0

$x\neq0$

Correct answer:

$y\geq0$

Explanation:

The square root of any number cannot be negative.

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Example Question #57 : Introduction To Functions

Absolutevalue

$\textup{What is the range of }y=\left | x\right |\textup{?}$

Possible Answers:

$x\geq0$

y>0

$y=\:all\:real\:numbers$

$y\geq0$

Correct answer:

$y\geq0$

Explanation:

The absolute value of a number cannot be negative.

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Example Question #51 : Functions And Graphs

Determine the domain of the following function:

$y=\frac{x^2+6x-4}{x-5}$

Possible Answers:

$x\le 16-2\sqrt{51}$ and $x \ge 2(8+\sqrt{51})$

$0\le x<\infty$

$-\infty<x<5$ and $5<x<\infty$

$-\infty <x<0$ and $0<x<\infty$

$-\infty <x<\infty$

Correct answer:

$-\infty<x<5$ and $5<x<\infty$

Explanation:

The domain is all the possible values of . To determine the domain, we need to determine what values don't work for this equation. The only value that is not allowed for this equation is 5, since that would make the denominator have a value of , and you can not divide by . Therefore, the domain of this equation is:

$-\infty < x<5$ and $5<x<\infty$

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Example Question #1 : How To Find The Domain Of A Function

Give the domain of the function:

$f(x) = \frac{x^{2} - 16}{x^{2}-6x+9}$

Possible Answers:

$\left \{ x |x \neq -3 \right \}$

$\left \{ x |x \neq -4 , x \neq 4 \right \}$

$\left \{ x | x \neq 3 \right \}$

$\left \{ x |x \neq -3 , x \neq 3 \right \}$

$\left \{ x | x\neq -4, x \neq 3, x\neq 4\right \}$

Correct answer:

$\left \{ x | x \neq 3 \right \}$

Explanation:

The domain of a rational function is the set of all values of for which the denominator is not equal to 0, so we set the denominator to 0 and solve for .

$x^{2} -6x + 9 = 0$

This is a quadratic function, so we factor the expression as (x+?)(x+?) , replacing the question marks with two numbers whose product is 9 and whose sum is . These numbers are -3,-3 , so

$x^{2} -6x + 9 = 0$

becomes

(x-3)(x-3) = 0 ,

or $(x-3)^{2} = 0$ .

This means that x-3=0 , or x = 3 .

Therefore, 3 is the only number excluded from the domain.

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Example Question #5 : How To Find The Domain Of A Function

Give the domain of the function:

$f(x) = \frac{x^{2} - 4}{x^{2}-6x+8}$

Possible Answers:

The set of all real numbers.

$\left \{x | x \neq -2, x \neq 2\ \right \}$

$\left \{x | x \neq 2 \right \}$

$\left \{x | x \neq -2, x \neq 2 ,x \neq 4 \right \}$

$\left \{x | x \neq 2 ,x \neq 4 \right \}$

Correct answer:

$\left \{x | x \neq 2 ,x \neq 4 \right \}$

Explanation:

The domain of a rational function is the set of all values of for which the denominator is not equal to 0 (the value of the numerator is irrelevant), so we set the denominator to 0 and solve for to find the excluded values.

$x^{2}-6x+8 =0$

This is a quadratic function, so we factor the expression as (x+?)(x+?) , replacing the question marks with two numbers whose product is 8 and whose sum is . These numbers are -4,-2 , so

$x^{2}-6x+8 =0$

becomes

(x-2)(x-4) = 0

So either

x-2 = 0 , in which case x = 2 ,

or x-4 = 0 , in which case x = 4 .

Therefore, 2 and 4 are the only numbers excluded from the domain.

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Algebra II : Functions and Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #51 : Introduction To Functions

Example Question #52 : Introduction To Functions

Example Question #53 : Introduction To Functions

Example Question #54 : Introduction To Functions

Example Question #55 : Introduction To Functions

Example Question #56 : Introduction To Functions

Example Question #57 : Introduction To Functions

Example Question #51 : Functions And Graphs

Example Question #1 : How To Find The Domain Of A Function

Example Question #5 : How To Find The Domain Of A Function

All Algebra II Resources

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