Clara Dennis

2022-11-04

Im need in graphing this log function: y=log1/4∣∣x2−5x+6∣∣
I found the intervals: (−∞,2), (2,3), (3,∞)
Should I just give x values and find y to graph this or is there another way?

kuthiwenihca

Expert

Use what you have computed:
On $\left(-\mathrm{\infty },2\right)\cup \left(3,\mathrm{\infty }\right)$ the polynomial ${x}^{2}-5x+6$ is positive. So, the function is equal to
${\mathrm{log}}_{1/4}\left({x}^{2}-5x+6\right)$
On (2,3) the polynomial ${x}^{2}-5x+6$ is negative. So, the function is equal to
${\mathrm{log}}_{1/4}\left(\left(x-2\right)\left(3-x\right)\right)$
Now, apply to each of these the procedure to determine the main elements of the graph.

Do you have a similar question?