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KIM [24]
3 years ago
8

The parent function of the function represented in the table is

Mathematics
1 answer:
kondor19780726 [428]3 years ago
4 0

Answer:

y=3^x+10

f(x)-values

decreased by 4

(4,87)

Step-by-step explanation:

The table shows the exponential growth function

y=a\cdot b^x +c

substitute some values to find a,b,c:

13=a\cdot b^1+c\\ \\19=a\cdot b^2 +c\\ \\37=a\cdot b^3+c

Subtract these equations:

ab^2+c-ab-c=19-13\Rightarrow ab(b-1)=6\\ \\ab^3+c-ab^2-c=37-19\Rightarrow ab^2(b-1)=18

Divide them:

\dfrac{ab^2(b-1)}{ab(b-1)}=\dfrac{18}{6}\Rightarrow b=3

Then

3a(3-1)=6\Rightarrow a=1

Hence,

13=1\cdot 3+c\Rightarrow c=10

Therefore, the parent function is y=3^x+10

If this function would be translated 4 units down, its expression will be

y=3^x+10-4\\ \\y=3^x+6

This means that f(x)-values decreased by 4.

Then the table for translated function is

\begin{array}{cccccc}x&1&2&3&4&5\\ \\f(x)&9&15&33&87&249\end{array}

The graph of translated function passes through the point (4,87)

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