The given function is a piecewise function with characteristics that vary with the value of x.
- Please find attached the graph of h(x).
Reasons:
The given information is presented as follows;
[tex]h(x) = \begin{cases} \mathbf{ \frac{1}{4}\cdot x-4}, & x\leq 0 \\ \mathbf{ \frac{1}{3}\cdot x-3}, & 0 < x \leq 3 \\ \mathbf{ \frac{1}{2}\cdot x-2}, & x \geq 4\end{cases}[/tex]
From the above piecewise function, we have;
For x ≤ 0, the slope of the graph of h(x) = [tex]\displaystyle \frac{1}{4}}[/tex]
For 0 < x ≤ 3, the slope of the graph of h(x) = [tex]\displaystyle \frac{1}{3}[/tex]
For x ≥ 4, the slope of the graph of h(x) = [tex]\displaystyle \frac{1}{2}[/tex]
Therefore, as we progress from left to right, the slope of h(x) increases and
the slope of the graph becomes steeper.
The graph of h(x) is plotted with the given equations using MS Excel as
shown in the attached diagram.
Learn more about piecewise functions here:
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