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
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)
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<span>
For the last blank, you're looking for an (x, f(x)) pair that is translated to (x, f(x)+5).
The car goes 23.2 miles every gallon, so with 15 gallons (15 * 23.2 = 348) it can go 348 miles. With the extra .25 that the car has, it can go 0.25 * 23.2 = 5.8 miles. 348 miles plus the 5.8 miles gets you 353.8 miles on 15.25 gallons.
