Graph f(x)=|4x|+5

Math
Find the absolute value vertex. In this case, the vertex for is .
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To find the coordinate of the vertex, set the inside of the absolute value equal to . In this case, .
Replace the variable with in the expression.
Simplify .
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Simplify each term.
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The absolute value is the distance between a number and zero. The distance between and is .
Multiply by .
Add and .
The absolute value vertex is .
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
Set-Builder Notation:
For each value, there is one value. Select few values from the domain. It would be more useful to select the values so that they are around the value of the absolute value vertex.
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Substitute the value into . In this case, the point is .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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The absolute value is the distance between a number and zero. The distance between and is .
Multiply by .
Add and .
The final answer is .
Substitute the value into . In this case, the point is .
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Replace the variable with in the expression.
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
The absolute value is the distance between a number and zero. The distance between and is .
Multiply by .
Add and .
The final answer is .
Substitute the value into . In this case, the point is .
Tap for more steps…
Replace the variable with in the expression.
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
The absolute value is the distance between a number and zero. The distance between and is .
Multiply by .
Add and .
The final answer is .
The absolute value can be graphed using the points around the vertex
Graph f(x)=|4x|+5

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