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
.

If function f was translated down 4 units, the
-values would be
.

A point in the table for the transformed function would be
.

Answer 1

Answer: I think this is it:

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 (4,87)

Step-by-step explanation: I got it right on Edmentum!

Answer 2

• 3^x
• 9, 15, 33, 87, 249
• (4, 87) for example

Explanation:

a) First differences of the f(x) values in the table are ...

19 -13 = 6, 37 -19 = 18, 91 -37 = 54, 253 -91 = 162

The second differences are not constant:

18 -6 = 12, 54 -18 = 36, 162 -54 = 108

But, we notice that both the first and second differences have a common ratio. This is characteristic of an exponential function. The common ratio is 18/6 = 3, so the parent function is 3^x.

__

b) Translating a function down 4 units subtracts 4 from each y-value. The values of f(x) in the table would be ...

9, 15, 33, 87, 249

__

c) The x-values of the function stay the same for a vertical translation, so the points in the table of the transformed function are ...

(x, f(x)) = (1, 9), (2, 15), (3, 33), (4, 87), (5, 249)