Question

select the correct answer from each drop - down menu.
the function f is given by the table of values as shown below.

x	1	2	3	4	5
f(x)	13	19	37	91	253

use the given table to complete the statements.
the parent function of the function represented in the table is exponential.
if function f was translated down 4 units, the f(x) - values would be decreased by 4.
a point in the table for the transformed function would be
(1,52)
(4,87)
(3,29)
(2,23)

Explanation:

Step1: Recall vertical translation rule

When a function \( y = f(x) \) is translated down by \( k \) units, the new function is \( y = f(x)-k \). Here, \( k = 4 \), so we subtract 4 from each \( f(x) \)-value.

Step2: Check each option

• For \( (1,52) \): Original \( f(1)=13 \), translated value \( 13 - 4=9

eq52 \).

• For \( (4,87) \): Original \( f(4)=91 \), translated value \( 91 - 4 = 87 \).
• For \( (3,29) \): Original \( f(3)=37 \), translated value \( 37 - 4 = 33

eq29 \).

• For \( (2,23) \): Original \( f(2)=19 \), translated value \( 19 - 4 = 15

eq23 \).

Answer:

(4,87)