Section 3.4 : The Definition of a Function
10. Given \(h\left( z \right) = \left\{ {\begin{array}{*{20}{l}}{3z}&{{\rm{if }}z < 2}\\{1 + {z^2}}&{{\rm{if }}z \ge 2}\end{array}} \right.\) determine each of the following.
- \(h\left( 0 \right)\)
- \(h\left( 2 \right)\)
- \(h\left( 7 \right)\)
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a \(h\left( 0 \right)\) Show SolutionRemember that for piecewise functions we use the equation for which the number in the parenthesis meets the condition.
For this problem we can see that \(0 < 2\) and so we use top equation to do the evaluation.
\[h\left( 0 \right) = 3\left( 0 \right) = \require{bbox} \bbox[2pt,border:1px solid black]{0}\]b \(h\left( 2 \right)\) Show Solution
Remember that for piecewise functions we use the equation for which the number in the parenthesis meets the condition.
For this problem we can see that \(2 \ge 2\) and so we use bottom equation to do the evaluation.
\[h\left( 2 \right) = 1 + {\left( 2 \right)^2} = \require{bbox} \bbox[2pt,border:1px solid black]{5}\]c \(h\left( 7 \right)\) Show Solution
Remember that for piecewise functions we use the equation for which the number in the parenthesis meets the condition.
For this problem we can see that \(7 \ge 2\) and so we use bottom equation to do the evaluation.
\[h\left( 7 \right) = 1 + {\left( 7 \right)^2} = \require{bbox} \bbox[2pt,border:1px solid black]{{50}}\]