To determine the values of the function [tex]\( h \)[/tex] at specific points, we need to evaluate the piecewise function given.
For [tex]\( x = 0 \)[/tex]:
When [tex]\( x = 0 \)[/tex], we use the second piece of the function since [tex]\( 0 \leq x < 4 \)[/tex]. The function is given by:
[tex]\[ h(x) = 2x^2 - 3x + 10 \][/tex]
Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[ h(0) = 2(0)^2 - 3(0) + 10 = 10 \][/tex]
For [tex]\( x = 4 \)[/tex]:
When [tex]\( x = 4 \)[/tex], we use the third piece of the function since [tex]\( x \geq 4 \)[/tex]. The function is given by:
[tex]\[ h(x) = 2^x \][/tex]
Substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[ h(4) = 2^4 = 16 \][/tex]
Therefore, the values of the function are:
[tex]\[
\begin{array}{l}
h(0) = 10 \\
h(4) = 16
\end{array}
\][/tex]
