Answer: Answer:
Step-by-step explanation:
a) First differences of the f(x) values in the table are ...
<u> 19 -13 = 6, 37 -19 = 18, 91 -37 = 54, 253 -91 = 162 </u>
The second differences are not constant:
<u> 18 -6 = 12, 54 -18 = 36, 162 -54 = 108 </u>
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 <u>3^x</u>
b) Translating a function down 4 units subtracts 4 from each y-value. The values of f(x) in the table would be ...
<u> 9, 15, 33, 87, 249</u>
<u />
<u>c)</u> The x-values of the function stay the same for a vertical translation, so the points in the table of the transformed function are ...<u> </u>
<u> (x, f(x)) = (1, 9), (2, 15), (3, 33), (4, 87), (5, 249)</u>
