anabelle17
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Consider the function [tex]$h$[/tex].

[tex]\[ h(x)=\left\{\begin{array}{ll}
3x - 4, & x \ \textless \ 0 \\
2x^2 - 3x + 10, & 0 \leq x \ \textless \ 4 \\
2^x, & x \geq 4
\end{array}\right. \][/tex]

What are the values of the function when [tex]$x = 0$[/tex] and when [tex]$x = 4$[/tex]?

[tex]\[
\begin{array}{l}
h(0) = \square \\
h(4) = \square
\end{array}
\][/tex]

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Sagot :

GinnyAnswer
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]
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