Question

The parent function of the function represented in the table is

Answer 1

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)