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The function [tex]$f$[/tex] is given by the table of values as shown below.
\begin{tabular}{|c|c|c|c|c|c|}
\hline[tex]$x$[/tex] & 1 & 2 & 3 & 4 & 5 \\
\hline[tex]$f(x)$[/tex] & 13 & 19 & 37 & 91 & 253 \\
\hline
\end{tabular}

Use the given table to complete the statements.

If the function [tex]$f$[/tex] was translated down 4 units, the [tex]$\square$[/tex]-values would be [tex]$\square$[/tex]. A point in the table for the transformed function would be [tex]$\square$[/tex].

Sagot :

GinnyAnsweridn
To solve this problem, we need to perform a vertical transformation of the function [tex]\( f \)[/tex] by translating it down 4 units. This means we subtract 4 from each value of [tex]\( f(x) \)[/tex] in the given table.

### Step 1: Translate the Function Down 4 Units

Let's start by transforming the values of [tex]\( f(x) \)[/tex] as follows:
- For [tex]\( x = 1 \)[/tex]: [tex]\( f(1) = 13 \)[/tex], so the new value will be [tex]\( 13 - 4 = 9 \)[/tex]
- For [tex]\( x = 2 \)[/tex]: [tex]\( f(2) = 19 \)[/tex], so the new value will be [tex]\( 19 - 4 = 15 \)[/tex]
- For [tex]\( x = 3 \)[/tex]: [tex]\( f(3) = 37 \)[/tex], so the new value will be [tex]\( 37 - 4 = 33 \)[/tex]
- For [tex]\( x = 4 \)[/tex]: [tex]\( f(4) = 91 \)[/tex], so the new value will be [tex]\( 91 - 4 = 87 \)[/tex]
- For [tex]\( x = 5 \)[/tex]: [tex]\( f(5) = 253 \)[/tex], so the new value will be [tex]\( 253 - 4 = 249 \)[/tex]

So, the transformed function values are [tex]\( 9, 15, 33, 87, 249 \)[/tex].

### Step 2: Find a Point in the Transformed Function

To verify our translation, let's take a specific point. Suppose we choose [tex]\( x = 1 \)[/tex]:
- Originally, [tex]\( f(1) = 13 \)[/tex]
- After translating down 4 units, the value becomes [tex]\( 13 - 4 = 9 \)[/tex]

Thus, the point [tex]\((1, 9)\)[/tex] will be a point in the table for the transformed function.

### Final Answer

- -values: The transformed function values are [tex]\( 9, 15, 33, 87, 249 \)[/tex]
- A point in the table for the transformed function would be: [tex]\((1, 9)\)[/tex]

Therefore, the correct answers are:
- The [tex]\( f \)[/tex]-values would be: [tex]\( 9, 15, 33, 87, 249 \)[/tex]
- A point in the table for the transformed function would be: [tex]\((1, 9)\)[/tex]
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