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

Sagot :

GinnyAnswer
To determine the values of the function [tex]\( h(x) \)[/tex] at [tex]\( x = 0 \)[/tex] and [tex]\( x = 4 \)[/tex], we need to refer to the piecewise definition of the function [tex]\( h \)[/tex].

1. For [tex]\( x = 0 \)[/tex]:
- Based on the definition, when [tex]\( 0 \leq x < 4 \)[/tex], the function [tex]\( h(x) = 2x^2 - 3x + 10 \)[/tex].
- Plug in [tex]\( x = 0 \)[/tex] into this part of the function:
[tex]\[ h(0) = 2(0)^2 - 3(0) + 10 \][/tex]
- Simplifying,
[tex]\[ h(0) = 0 - 0 + 10 = 10 \][/tex]

2. For [tex]\( x = 4 \)[/tex]:
- Based on the definition, when [tex]\( x \geq 4 \)[/tex], the function [tex]\( h(x) = 2^x \)[/tex].
- Plug in [tex]\( x = 4 \)[/tex] into this part of the function:
[tex]\[ h(4) = 2^4 \][/tex]
- Simplifying,
[tex]\[ h(4) = 16 \][/tex]

Thus, the values of the function are:
[tex]\[ \begin{array}{l} h(0) = 10 \\ h(4) = 16 \end{array} \][/tex]
beto05202008

Answer:

To determine the values of the function \( h(x) \) at \( x = 0 \) and \( x = 4 \), we need to refer to the piecewise definition of the function \( h \).

1. For \( x = 0 \):

- Based on the definition, when \( 0 \leq x < 4 \), the function \( h(x) = 2x^2 - 3x + 10 \).

- Plug in \( x = 0 \) into this part of the function:

\[

    h(0) = 2(0)^2 - 3(0) + 10

    \]

- Simplifying,

\[

    h(0) = 0 - 0 + 10 = 10

    \]

2. For \( x = 4 \):

- Based on the definition, when \( x \geq 4 \), the function \( h(x) = 2^x \).

- Plug in \( x = 4 \) into this part of the function:

\[

    h(4) = 2^4

    \]

- Simplifying,

\[

    h(4) = 16

    \]

Thus, the values of the function are:

\[

\begin{array}{l}

h(0) = 10 \n

h(4) = 16

\end{array}

\]

Step-by-step explanation:

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