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### 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.

1. $$h\left( 0 \right)$$
2. $$h\left( 2 \right)$$
3. $$h\left( 7 \right)$$

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a $$h\left( 0 \right)$$ 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 $$0 < 2$$ 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.

$h\left( 7 \right) = 1 + {\left( 7 \right)^2} = \require{bbox} \bbox[2pt,border:1px solid black]{{50}}$