Let's analyze the given information and break down the steps to complete the statements.
Step 1: Identify the Parent Function
The given values for [tex]\( f(x) \)[/tex] suggest rapid growth which is characteristic of an exponential function. Therefore, the parent function of the function represented in the table is:
[tex]\[ \text{exponential} \][/tex]
Step 2: Translate the Function Down
To translate the function [tex]\( f \)[/tex] down by 4 units, subtract 4 from each [tex]\( f(x) \)[/tex].
Given the original [tex]\( f(x) \)[/tex] values:
[tex]\[ f(1) = 13, \quad f(2) = 19, \quad f(3) = 37, \quad f(4) = 91, \quad f(5) = 253 \][/tex]
Translating these down by 4 units:
[tex]\[ f(1) - 4 = 9, \quad f(2) - 4 = 15, \quad f(3) - 4 = 33, \quad f(4) - 4 = 87, \quad f(5) - 4 = 249 \][/tex]
So, the [tex]\( y \)[/tex]-values (f(x) values) would be:
[tex]\[ 9, 15, 33, 87, 249 \][/tex]
Step 3: Identify a Point in the Transformed Function
Select a specific point in the table for the transformed function for a given [tex]\( x \)[/tex] value.
For [tex]\( x = 3 \)[/tex]:
The transformed [tex]\( f(x) \)[/tex] value is:
[tex]\[ f(3) = 33 \][/tex]
Therefore, a point in the table for the transformed function would be:
[tex]\[ (3, 33) \][/tex]
Summary of the Solutions:
1. The parent function of the function represented in the table is:
[tex]\[ \text{exponential} \][/tex]
2. If function [tex]\( f \)[/tex] was translated down 4 units, the [tex]\( y \)[/tex]-values would be:
[tex]\[ 9, 15, 33, 87, 249 \][/tex]
3. A point in the table for the transformed function would be:
[tex]\[ (3, 33) \][/tex]
Now, completing the statements in the problem:
The parent function of the function represented in the table is [tex]\(\boxed{\text{exponential}}\)[/tex]
If function [tex]\( f \)[/tex] was translated down 4 units, the [tex]\(\boxed{y}\)[/tex]-values would be [tex]\(\boxed{9, 15, 33, 87, 249}\)[/tex]
A point in the table for the transformed function would be [tex]\(\boxed{(3, 33)}\)[/tex]
