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



Answer :

GinnyAnswer
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]

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