Question

Plz help me on this

Answer 1

1) The parent function of the function represented in the table
x2-x1=2-1→x2-x1=1, f(2)-f(1)=11-9→f(2)-f(1)=2
x3-x2=3-2→x3-x2=1=x2-x1, f(3)-f(2)=15-11→f(3)-f(2)=4 different to f(2)-f(1)=2
The function is not linear

[f(3)-f(2)]-[f(2)-f(1)]=4-2=2
x4-x3=4-3→x4-x3=1=x3-x2=x2-x1
f(4)-f(3)=23-15→f(4)-f(3)=8
[f(4)-f(3)]-[f(3)-f(2)]=8-4=4 > 2=[f(3)-f(2)]-[f(2)-f(1)]

Answer: The parent function of the function represented in the table is exponential.

2) If function f was translated up 5 units, the f(x) - values would be increased by 5.

3) The points in the table for the transformed function would be:
(1,9+5)=(1,14)
(2,11+5)=(2,16)
(3,15+5)=(3,20)
(4,23+5)=(4,28)
(5,39+5)=(5,44)
Answer: A point in the table for the transformed function would be (2,16)

Answer 2

First differences are 2, 4, 8, 16, which is a geometric sequence. The parent function is not linear (constant first difference) or quadratic (first difference increases by the same amount from one to the next). When the first differences are a geometric sequence, the underlying sequence is a geometric (exponential) sequence.

1st blank: exponential

Translation up adds a constant to each of the f(x) values.

2nd blank: f(x)
3rd blank: increased by 5

For the last blank, you're looking for an (x, f(x)) pair that is translated to (x, f(x)+5).

4th blank: (2, 16)