How to graph an absolute value function - Algebra 1

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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 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.$

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