Let's evaluate the function \( h(x) \) at the specified points \( x = 0 \) and \( x = 4 \).
1. Evaluating \( h(0) \):
According to the piecewise function definition, when \( 0 \leq x < 4 \), we use the formula:
[tex]\[ h(x) = 2x^2 - 3x + 10 \][/tex]
For \( x = 0 \):
[tex]\[ h(0) = 2(0)^2 - 3(0) + 10 = 0 - 0 + 10 = 10 \][/tex]
2. Evaluating \( h(4) \):
According to the piecewise function definition, when \( x \geq 4 \), we use the formula:
[tex]\[ h(x) = 2^x \][/tex]
For \( x = 4 \):
[tex]\[ h(4) = 2^4 = 16 \][/tex]
Thus, the values of the function are:
[tex]\[ h(0) = 10 \][/tex]
[tex]\[ h(4) = 16 \][/tex]
