Graphing Absolute Value Functions

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Notes

Notes for Absolute Value Parent Function

\({\text{Transformations of Absolute Value Functions}}\)
\(\underline{\text{Function/Transformation}}\) \(\underline{\text{Description}}\)
\(|x|\)
\(\text{Parent Function}\)
\(|x+h|\)
\(\text{Translated } h \text{ units left}\)
\(|x-h|\)
\(\text{Translated } h \text{ units right}\)
\(|x|+k\)
\(\text{Translated } k \text{ units up}\)
\(|x|-k\)
\(\text{Translated } k \text{ units down}\)
\(a \cdot |x|\)
\(\text{Vertical dilation (stretch) by a factor of } a \)
\(\frac{1}{a} \cdot |x|\)
\(\text{Vertical dilation (shrink) by a factor of } \frac{1}{a}\)
\(|b \cdot x|\)
\(\text{horizontal dilation (shrink) by a factor of } \frac{1}{b} \)
\(\left|\frac{1}{b} \cdot x\right|\)
\(\text{horizontal dilation (stretch) by a factor of }b \)
\(-|x|\)
\(\text{Reflection over x-axis}\)
\(|-x|\)
\(\text{Reflection over y-axis}\)


Questions

Graph the following absolute value functions

\(\textbf{1)}\) \( f(x)=|x|+3\)Link to Youtube Video Solving Question Number 1


\(\textbf{2)}\) Find the domain and range of \(f(x)=|x|+3\) Link to Youtube Video Solving Question Number 2


\(\textbf{3)}\) \(f(x)=2|x|-4\)Link to Youtube Video Solving Question Number 3


\(\textbf{4)}\) \(f(x)=-|2x|\)Link to Youtube Video Solving Question Number 4


\(\textbf{5)}\) \(f(x)=|x+3|+2\)Link to Youtube Video Solving Question Number 5


\(\textbf{6)}\) \(f(x)=|.5x|+1\)Link to Youtube Video Solving Question Number 6



See Related Pages\(\)

\(\bullet\text{ Interactive Absolute Value Grapher}\)
\(\,\,\,\,\,\,\,\,\text{(Desmos.com)}\)
\(\bullet\text{ Graphing Quadratic Functions}\)
\(\,\,\,\,\,\,\,\,f(x)= f(x)=(x+3)^2-2 \) Thumbnail for Graphing Quadratic Functions
\(\bullet\text{ Graphing Square Root Functions}\)
\(\,\,\,\,\,\,\,\,\)Notes for Graphing Square Root Functions
\(\bullet\text{ Graphing Cube Root Functions}\)
\(\,\,\,\,\,\,\,\,\)Notes for Graphing Cube Root Functions


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