MATH SOLVE

5 months ago

Q:
# Select the correct answer from each drop-down menu.x 1 2 3 4 5f(x) 9 11 15 23 39The function f is given by the table of values as shown below.Use the given table to complete the statements.The parent function of the function represented in the table is exponential, quadratic, or linear .If function f was translated up 5 units, the f(x), x, or x and f(x) -values would be divided by 5, multiplied by 5, decreased by 5, or increased by 5 .A point in the table for the transformed function would be (2, 16), (4, 18), (3, 5), or (1, 45) .

Accepted Solution

A:

Let us examine the speed of growth of the function. We have that the difference between successive terms is: 2, 4, 8, 16. These are powers of 2 and thus there is clearly an exponential increase in the parent function. In fact, the function can be modeled by f(x)=C+2^x where C is a constant.

We have that the new function is g(x). Translating upwards by 5 means that the new y-values are 5 units higher. Hence, we have that the pairs (x,f(x)) correspond to the pairs (x,f(x)+5) and thus the answer is that the f(x)/y-values will be increased by 5.

According to the above, we need to check the given values and see whether in some cases we have g(x)=f(x)+5; in layman's terms, we need to check whether for some x, the new y-value is bigger by 5 from the old one. This is the case only for (2,16) since the old point was (2,11).

We have that the new function is g(x). Translating upwards by 5 means that the new y-values are 5 units higher. Hence, we have that the pairs (x,f(x)) correspond to the pairs (x,f(x)+5) and thus the answer is that the f(x)/y-values will be increased by 5.

According to the above, we need to check the given values and see whether in some cases we have g(x)=f(x)+5; in layman's terms, we need to check whether for some x, the new y-value is bigger by 5 from the old one. This is the case only for (2,16) since the old point was (2,11).