Let's determine the values of the function \( h \) at \( x = 0 \) and \( x = 4 \) by analyzing the piecewise function and plugging these values directly into the appropriate pieces.
For \( x = 0 \):
The function \( h \) is defined as \( h(x) = 2x^2 - 3x + 10 \) for \( 0 \leq x < 4 \). Therefore, we can substitute \( x = 0 \) into this expression:
[tex]\[ h(0) = 2(0)^2 - 3(0) + 10 = 0 - 0 + 10 = 10 \][/tex]
So, \( h(0) = 10 \).
For \( x = 4 \):
The function \( h \) is defined as \( h(x) = 2^x \) for \( x \geq 4 \). Therefore, we can substitute \( x = 4 \) into this expression:
[tex]\[ h(4) = 2^4 = 16 \][/tex]
So, \( h(4) = 16 \).
Thus, the values of the function are:
[tex]\[ h(0) = 10 \][/tex]
[tex]\[ h(4) = 16 \][/tex]
