Given the piecewise function [tex]\( h(x) \)[/tex]:
[tex]\[ h(x) = \begin{cases}
3x - 4, & \text{if } x < 0 \\
2x^2 - 3x + 10, & \text{if } 0 \leq x < 4 \\
2^x, & \text{if } x \geq 4
\end{cases} \][/tex]
We need to find the values of the function when [tex]\( x = 0 \)[/tex] and [tex]\( x = 4 \)[/tex].
1. For [tex]\( x = 0 \)[/tex]:
Since [tex]\( 0 \leq x < 4 \)[/tex], we use the second piece of the function:
[tex]\[ h(0) = 2(0)^2 - 3(0) + 10 = 0 - 0 + 10 = 10 \][/tex]
2. For [tex]\( x = 4 \)[/tex]:
Since [tex]\( x \geq 4 \)[/tex], we use the third piece of the function:
[tex]\[ h(4) = 2^4 = 16 \][/tex]
Therefore, the values of the function are:
[tex]\[ h(0) = 10 \][/tex]
[tex]\[ h(4) = 16 \][/tex]
