How to graph an absolute value function - Algebra

Card 0 of 54

Question

Which of these would most likely be the equation corresponding to the above graph?

Answer

This is an absolute value graph. Its equation takes the form , in which represent the number of units that the base graph is translated right and up respectively.

Since the graph of is translated three units left and six units down, and .

Plug these values into the general form of the equation:

Simplify:

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Question

Which of these would most likely be the equation corresponding to the above graph?

Answer

This is an absolute value graph. Its equation takes the form , in which represent the number of units that the base graph is translated right and up respectively.

Since the graph of is translated two units right and one unit down, and , so the equation would be:

or

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Question

Give the -intercept(s) of the graph of the function $f(x) = 7 - \left | 2x-3 \right |$

Answer

To find the -intercept(s) of the graph, set and solve for .

$f(x) = 7 - \left | 2x-3 \right |$

$0= 7 - \left | 2x-3 \right |$

$0 + \left | 2x-3 \right |= 7 - \left | 2x-3 \right | + \left | 2x-3 \right |$

$\left | 2x-3 \right |= 7$

Rewrite this as the compound equation:

or

Solve each separately:

$2x \div 2 = -4\div 2$

$2x \div 2 = 10\div 2$

There are two -intercepts:

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Question

$\textup{Find the lowest attainable value of }y \textup{ in } y=-4+ \left |4x^2-25 \right |.$

Answer

$\ \left | 4x^2-25\right | \textup{cannot get any lower than zero,}\\textup{so\textit{ y} cannot get any lower than} -4.$

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Question

$\textup{What is the slope of } y=-4\left | x-2\right | \textup{ when } x=1?$

Answer

$\textup{When }x=1\textup{ the expression inside the absolute value is negative,} \\textup{so the function can be written as } y=-4(2-x)=4x-8,\textup{ with a slope of 4.}\\textup{Plus, the slope changes to -4 when } x>2. \textup{ When } x=2 \textup{ it does not exist.}$

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Question

$\textup{Which is an \textit{x}-intercept of the function } y=\left | -x^2-8x-16\right |-4.$

Answer

$\ \textup{The function can be simplified as } \y=\left | -(x+4)^2\right |-4=\left |(x+4)^2\right |-4=(x+4)^2-4.\\textup{In order to find the \textit{x}-intercecpt, we solve the equation}\0=(x+4)^2-4 \textup{ which becomes }\(x+4)=\pm2\textup{ and has solution } -2 \textup{ and } -6.$

Compare your answer with the correct one above

Question

Which of these would most likely be the equation corresponding to the above graph?

Answer

This is an absolute value graph. Its equation takes the form , in which represent the number of units that the base graph is translated right and up respectively.

Since the graph of is translated three units left and six units down, and .

Plug these values into the general form of the equation:

Simplify:

Compare your answer with the correct one above

Question

Which of these would most likely be the equation corresponding to the above graph?

Answer

This is an absolute value graph. Its equation takes the form , in which represent the number of units that the base graph is translated right and up respectively.

Since the graph of is translated two units right and one unit down, and , so the equation would be:

or

Compare your answer with the correct one above

Question

Give the -intercept(s) of the graph of the function $f(x) = 7 - \left | 2x-3 \right |$

Answer

To find the -intercept(s) of the graph, set and solve for .

$f(x) = 7 - \left | 2x-3 \right |$

$0= 7 - \left | 2x-3 \right |$

$0 + \left | 2x-3 \right |= 7 - \left | 2x-3 \right | + \left | 2x-3 \right |$

$\left | 2x-3 \right |= 7$

Rewrite this as the compound equation:

or

Solve each separately:

$2x \div 2 = -4\div 2$

$2x \div 2 = 10\div 2$

There are two -intercepts:

Compare your answer with the correct one above

Question

$\textup{Find the lowest attainable value of }y \textup{ in } y=-4+ \left |4x^2-25 \right |.$

Answer

$\ \left | 4x^2-25\right | \textup{cannot get any lower than zero,}\\textup{so\textit{ y} cannot get any lower than} -4.$

Compare your answer with the correct one above

Question

$\textup{What is the slope of } y=-4\left | x-2\right | \textup{ when } x=1?$

Answer

$\textup{When }x=1\textup{ the expression inside the absolute value is negative,} \\textup{so the function can be written as } y=-4(2-x)=4x-8,\textup{ with a slope of 4.}\\textup{Plus, the slope changes to -4 when } x>2. \textup{ When } x=2 \textup{ it does not exist.}$

Compare your answer with the correct one above

Question

$\textup{Which is an \textit{x}-intercept of the function } y=\left | -x^2-8x-16\right |-4.$

Answer

$\ \textup{The function can be simplified as } \y=\left | -(x+4)^2\right |-4=\left |(x+4)^2\right |-4=(x+4)^2-4.\\textup{In order to find the \textit{x}-intercecpt, we solve the equation}\0=(x+4)^2-4 \textup{ which becomes }\(x+4)=\pm2\textup{ and has solution } -2 \textup{ and } -6.$

Compare your answer with the correct one above

Question

Which of these would most likely be the equation corresponding to the above graph?

Answer

This is an absolute value graph. Its equation takes the form , in which represent the number of units that the base graph is translated right and up respectively.

Since the graph of is translated three units left and six units down, and .

Plug these values into the general form of the equation:

Simplify:

Compare your answer with the correct one above

Question

Which of these would most likely be the equation corresponding to the above graph?

Answer

This is an absolute value graph. Its equation takes the form , in which represent the number of units that the base graph is translated right and up respectively.

Since the graph of is translated two units right and one unit down, and , so the equation would be:

or

Compare your answer with the correct one above

Question

Give the -intercept(s) of the graph of the function $f(x) = 7 - \left | 2x-3 \right |$

Answer

To find the -intercept(s) of the graph, set and solve for .

$f(x) = 7 - \left | 2x-3 \right |$

$0= 7 - \left | 2x-3 \right |$

$0 + \left | 2x-3 \right |= 7 - \left | 2x-3 \right | + \left | 2x-3 \right |$

$\left | 2x-3 \right |= 7$

Rewrite this as the compound equation:

or

Solve each separately:

$2x \div 2 = -4\div 2$

$2x \div 2 = 10\div 2$

There are two -intercepts:

Compare your answer with the correct one above

Question

$\textup{Find the lowest attainable value of }y \textup{ in } y=-4+ \left |4x^2-25 \right |.$

Answer

$\ \left | 4x^2-25\right | \textup{cannot get any lower than zero,}\\textup{so\textit{ y} cannot get any lower than} -4.$

Compare your answer with the correct one above

Question

$\textup{What is the slope of } y=-4\left | x-2\right | \textup{ when } x=1?$

Answer

$\textup{When }x=1\textup{ the expression inside the absolute value is negative,} \\textup{so the function can be written as } y=-4(2-x)=4x-8,\textup{ with a slope of 4.}\\textup{Plus, the slope changes to -4 when } x>2. \textup{ When } x=2 \textup{ it does not exist.}$

Compare your answer with the correct one above

Question

$\textup{Which is an \textit{x}-intercept of the function } y=\left | -x^2-8x-16\right |-4.$

Answer

$\ \textup{The function can be simplified as } \y=\left | -(x+4)^2\right |-4=\left |(x+4)^2\right |-4=(x+4)^2-4.\\textup{In order to find the \textit{x}-intercecpt, we solve the equation}\0=(x+4)^2-4 \textup{ which becomes }\(x+4)=\pm2\textup{ and has solution } -2 \textup{ and } -6.$

Compare your answer with the correct one above

Question

Which of these would most likely be the equation corresponding to the above graph?

Answer

This is an absolute value graph. Its equation takes the form , in which represent the number of units that the base graph is translated right and up respectively.

Since the graph of is translated three units left and six units down, and .

Plug these values into the general form of the equation:

Simplify:

Compare your answer with the correct one above

Question

Which of these would most likely be the equation corresponding to the above graph?

Answer

This is an absolute value graph. Its equation takes the form , in which represent the number of units that the base graph is translated right and up respectively.

Since the graph of is translated two units right and one unit down, and , so the equation would be:

or

Compare your answer with the correct one above

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