Using the graph identify the intervals:
a) Function being less than or equal to 0: In which x interval is the graph under the x-axis (the functions are less than 0 when they are under x-axis)
As the ineqaulity sing is less than or equal to 0, the interval includes those x-values for which the function is 0:
Solution: Interval from x=1 to x=3
[tex]\begin{gathered} x^2-4x+3\leq0 \\ 1\leq x\leq3 \\ \lbrack1,3\rbrack \end{gathered}[/tex]b) Function being greater than or equal to 0: In which x interval is the graph over the x-axis.
As the ineqaulity sing is greater than or equal to 0, the interval includes those x-values for which the function is 0:
Solution: Interval from - infinite to 1 and from 3 to infinite
[tex]\begin{gathered} x^2-4x+3\ge0 \\ 1\ge x\ge3 \\ (-\infty,1\rbrack\cup\lbrack3,\infty) \end{gathered}[/tex]c) Function being greater than 0: In which x interval is the graph over the x-axis.
As the ineqaulity sing is greater than to 0, the interval does not include those x-values for which the function is 0.
[tex]\begin{gathered} x^2-4x+3>0 \\ 1>x>3 \\ (-\infty,1)\cup(3,\infty) \end{gathered}[/tex]d) Function being less than 0: In which x interval is the graph under the x-axis.
As the ineqaulity sing is less than 0, the interval does not include those x-values for which the function is 0:
[tex]\begin{gathered} x^2-4x+3<0 \\ 1