Question

What is the equation of the function shown in the graph, given that the equation of the parent function is f(x)=(1/7)^x ?


A. g(x)=(1/7)^x−3

B. g(x)=(1/7)^x−2

C. g(x)=(1/7)^x−4

D. g(x)=(1/7)^x+3

Answer 1

Answer:

$g(x) = (\frac{1}{7} )^{x} - 4$

Step-by-step explanation:

The graph of a function is shown in the diagram attached.

The parent function is $f(x) = (\frac{1}{7} )^{x}$ ........ (1)

Now, from the equation of the parent function at x = 0, y = 1.

But in the graph, the curve intersects y-axis at point (0,-3) point.

So, there is a translation of the parent function (1) by [1 - ( - 3)] = 4 units vertically downward.

Therefore, the graphed function is $g(x) = (\frac{1}{7} )^{x} - 4$ (Answer)