kylorensimp
Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Type the correct answer in each box. Use numerals instead of words.

The function [tex]$f$[/tex] is given by the table of values shown below:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 0 & 1 & 2 & 3 \\
\hline
$f(x)$ & 0 & 2 & 8 & 26 \\
\hline
\end{tabular}
\][/tex]

If function [tex]$f$[/tex] is shifted vertically down by 2 units to obtain function [tex]$g$[/tex], complete the table of values which represents function [tex]$g$[/tex]:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 0 & 1 & 2 & 3 \\
\hline
$g(x)$ & \boxed{-2} & \boxed{0} & \boxed{6} & \boxed{24} \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnswer
To find the values of [tex]\( g(x) \)[/tex] when the function [tex]\( f(x) \)[/tex] is shifted vertically down by 2 units, we need to subtract 2 from each value of [tex]\( f(x) \)[/tex].

Given the table of values for [tex]\( f(x) \)[/tex]:

[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline f(x) & 0 & 2 & 8 & 26 \\ \hline \end{array} \][/tex]

The corresponding [tex]\( g(x) \)[/tex] values can be calculated as follows:

1. For [tex]\( x = 0 \)[/tex]:
[tex]\[ f(0) = 0 \\ g(0) = f(0) - 2 = 0 - 2 = -2 \][/tex]

2. For [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = 2 \\ g(1) = f(1) - 2 = 2 - 2 = 0 \][/tex]

3. For [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = 8 \\ g(2) = f(2) - 2 = 8 - 2 = 6 \][/tex]

4. For [tex]\( x = 3 \)[/tex]:
[tex]\[ f(3) = 26 \\ g(3) = f(3) - 2 = 26 - 2 = 24 \][/tex]

Thus, the table of values for [tex]\( g(x) \)[/tex] is:

[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline g(x) & -2 & 0 & 6 & 24 \\ \hline \end{array} \][/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.