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Algebra II : Functions and Graphs

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Example Question #13 : Domain And Range

What is the domain of the following function? Please use interval notation.

$y=\left | -x\right |$

Possible Answers:

$(-\infty ,0)$

$(0,\infty )$

$(-\infty ,\infty )$

Correct answer:

$(-\infty ,\infty )$

Explanation:

A basic knowledge of absolute value and its functions is valuable for this problem. However, if you do not know what the typical shape of an absoluate value function looks like, one can always plug in values and plot points.

Upon doing so, we learn that the -values (domain) are not restricted on either end of the function, creating a domain of negative infinity to postive infinity.

If we plug in -100000 for , we get 100000 for .

If we plug in 100000 for , we get 100000 for .

Additionally, if we plug in any value for , we will see that we always get a real, defined value for .

**Extra Note: Due to the absolute value notation, the negative (-) next to the is not important, in that it will always be made positive by the absolute value, making this function the same as $y=\left | x\right |$ . If the negative (-) was outside of the absolute value, this would flip the function, making all corresponding -values negative. However, this knowledge is most important for range, rather than domain.

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Example Question #14 : Domain And Range

Use the following function and domain to answer this question

f(x)=.25x+.38

$\left \{ 2,4,6,8,10 \right \}$

Find the range of the function for the given doman. Are and directly or inversely related?

Possible Answers:

$\left \{ .38, 1.88, 2.38, 3.88, 4.38 \right \}, direct$

$\left \{ .88,1.38,1.88, 2.38, 2.88 \right \}, direct$

$\left \{ .88,1.38,1.88, 2.38, 2.88 \right \}, inverse$

$\left \{ .38, 1.88, 2.38, 3.88, 4.38 \right \}, inverse$

Correct answer:

$\left \{ .88,1.38,1.88, 2.38, 2.88 \right \}, direct$

Explanation:

To find the range, plug each value of the domain into the equation:

$f(2)=.25(2)+.38 = {\color{Red} .88}$

$f(4)=.25(4)+.38 = {\color{Red} 1.38}$

$f(6)=.25(6)+.38={\color{Red} 1.88}$

$f(8)=.25(8)+.38={\color{Red} 2.38}$

$f(10)=.25(10)+.38={\color{Red} 2.88}$

As the x-values increase, the y-values do as well. Therefore there is a ${\color{Red} direct}$ relationship

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Example Question #15 : Domain And Range

Find the range of the function f(x): 4 + 0.75x for the domain $\left \{ {0,12,20,28} \right \}$ .

Possible Answers:

$\left \{ {0,5,11,16} \right \}$

$\left \{ {0,4,12,16} \right \}$

$\left \{ {4,5,9,16} \right \}$

$\left \{ {4,13,19,25} \right \}$

$\left \{ {0,9,16,21} \right \}$

Correct answer:

$\left \{ {4,13,19,25} \right \}$

Explanation:

The range of a function is the group of corresponding values for a given domain ( values). Plug each value into the function to find the range:

y_1=4+0.75(0)=4

y_2=4+0.75(12)=13

y_3=4+0.75(20)=19

y_4=4+0.75(28)=25

The range is $\left \{ {4,13,19,25} \right \}$ .

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Example Question #16 : Domain And Range

A function has the following range:

$\left \{ 2,5,7,8 \right \}$

Which of the following CANNOT be the domain of the function.

Possible Answers:

$\left \{ 1,2,3,4 \right \}$

$\left \{ 21,19,17,15 \right \}$

$\left \{ -2,-1,0,1 \right \}$

$\left \{ 2,6,7,7 \right \}$

$\left \{ 10,14,19,20 \right \}$

Correct answer:

$\left \{ 2,6,7,7 \right \}$

Explanation:

Functions cannot have more than one value for each value. This means different numbers in the range cannot be assigned to the same value in the domain. Therefore, ${\color{Red} \left \{ 2,6,7,7 \right \}}$ cannot be the domain of the function.

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Example Question #17 : Domain And Range

What is the range of the following function? Please use interval notation.

$y=-\left | x\right |$

Possible Answers:

$(0,-\infty )$

$(0,\infty )$

$(-\infty ,\infty )$

$(-\infty,0]$

Correct answer:

$(-\infty,0]$

Explanation:

Upon doing so, we learn that the -values (range) never surpass . This is because of the negative that is placed outside of the absolute value function. Meaning, for every value we plug in, we will always get a negative value for , except when x=0, y=0 .

With this knowledge, we can now confidently state the range as $(-\infty ,0]$

**Extra note: the negative sign outside of the absolute value is simply a transformation of $y=\left | x\right |$ , reflecting the function about the -axis.

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Example Question #41 : Functions And Graphs

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

Possible Answers:

$x\neq0$

$y= all \:real \: numbers$

$x= all \:real \: numbers$

x>0

y>0

Correct answer:

$x= all \:real \: numbers$

Explanation:

All inputs are valid. There is nothing you can put in for x that won't work.

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Example Question #42 : Functions And Graphs

Parabola

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

Possible Answers:

$x\geq0$

$x= all \:real \: numbers$

y>0

x>0

Correct answer:

$x= all \:real \: numbers$

Explanation:

All inputs are valid. There is nothing you can put in for x that won't work.

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Example Question #43 : Functions And Graphs

Cubing

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

Possible Answers:

-1<x<1

$x= all \:real \: numbers$

x>0

$y= all \:real \: numbers$

Correct answer:

$x= all \:real \: numbers$

Explanation:

All inputs are valid. There is nothing you can put in for x that won't work.

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Example Question #21 : Domain And Range

Absolutevalue

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

Possible Answers:

y>0

$x\neq0$

$x\geq0$

$x= all \:real \: numbers$

Correct answer:

$x= all \:real \: numbers$

Explanation:

All inputs are valid. There is nothing you can put in for x that won't work.

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Example Question #22 : Domain And Range

Exponential

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

Possible Answers:

y>0

$x= all \:real \: numbers$

$x\neq0$

x>0

Correct answer:

$x= all \:real \: numbers$

Explanation:

All inputs are valid. There is nothing you can put in for x that won't work.

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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 #13 : Domain And Range

Example Question #14 : Domain And Range

Example Question #15 : Domain And Range

Example Question #16 : Domain And Range

Example Question #17 : Domain And Range

Example Question #41 : Functions And Graphs

Example Question #42 : Functions And Graphs

Example Question #43 : Functions And Graphs

Example Question #21 : Domain And Range

Example Question #22 : Domain And Range

All Algebra II Resources

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