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Consider the function \( h \):
[tex]\[
h(x) =
\begin{cases}
3x - 4, & x \ \textless \ 0 \\
2x^2 - 3x + 10, & 0 \leq x \ \textless \ 4 \\
2^x, & x \geq 4
\end{cases}
\][/tex]

What are the values of the function when \( x = 0 \) and when \( x = 4 \)?
[tex]\[
\begin{array}{l}
h(0) = \square \\
h(4) = \square
\end{array}
\][/tex]

Sagot :

GinnyAnswer
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]
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