4.2 Transformation of graphs by modulus function  (Page 3/4)

Problem : Draw graph of $y=\left|\cos x\right|$ .

Solution : We first draw the graph of $y=\cos x$ . Then, we take the mirror image of lower half of the graph in x-axis and remove lower half of the graph to complete the construction of graph of $y=\left|\cos x\right|$

Problem : Draw graph of $y=|x^2-2x-3|$

Solution : We first draw graph $y=x^2-2x-3$ . The roots of corresponding quadratic equation are -1 and 3. After plotting graph of quadratic function, we take the mirror image of lower half of the graph in x-axis and remove lower half of the graph to complete the construction of graph of $y=|x^2-2x-3|$

Problem : Draw graph of $y=\left|{\log }_{10}x\right|$ .

Solution : We first draw graph $y={\log }_{10}x$ . Then, we take the mirror image of lower half of the graph in x-axis and remove lower half of the graph to complete the construction of graph of $y=\left|{\log }_{10}x\right|$ .

Problem : Draw graph of $\left|y\right|=\left(x-1\right)\left(x-3\right)$ .

Solution : We first draw the graph of quadratic function given by $y=\left(x-1\right)\left(x-3\right)$ . Then, we remove lower half of the graph and take mirror image of upper half of the graph in x-axis to complete the construction of graph of $\left|y\right|=\left(x-1\right)\left(x-3\right)$ .

Problem : Draw graph of $$\left|y\right|={\tan }^{-1}x$$ .

Solution : We first draw the graph of function given by $y={\tan }^{-1}x$ . Then, we remove lower half of the graph and take mirror image of upper half of the graph in x-axis to complete the construction of graph of $y={\tan }^{-1}x$ .