Question

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: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)

i hope this helps

Answer 2

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).

In Mathematics, the finite differences between the y-values of any quadratic function on equal intervals would always differ by a common numerical value.

For this table of values, the first finite difference and second finite differences can be calculated as follows:

First difference Second difference Common ratio

19 - 13 = 6

37 - 19 = 18 18 - 6 = 12 18/6 = 3

91 - 37 = 54 54 - 18 = 36 54/18 = 3

253 - 91 = 162 162 - 54 = 108 162/54 = 3

Therefore, this table of values represents an exponential function because the ratios are constant and common, which is a constant value of 3.

If any function f was translated down 4 units, it ultimately implies that the f(x)-values or y-values would be decreased by 4. By translating the point (4, 91) down 4 units, a point for the transformed function is given by:

(x, y) → (x', y' - 4)

(4, 91) → (4, 91 - 4) = (4, 87).