Question

Which function is shown in the graph below?

Answer 1

Answer:b

Step-by-step explanation: you graph each answer choice and see which one looks like the graph

Answer 2

Answer:  The correct option is

(B) $y=\left(\dfrac{1}{2}\right)^{x-3}+1.$

Step-by-step explanation:  We are given to select the function that is shown in the graph.

From the graph, we know that

if the function is represented by y = f(x), then f(0) = 9. That is, the value of y at x = 0 is 9.

Option (A) :  Here, the given function is

$y=\left(\dfrac{1}{2}\right)^{x+3}-1.$

So, at x = 0, the value of y is given by

$y(x=0)=\left(\dfrac{1}{2}\right)^{0+3}-1=\dfrac{1}{8}-1=-\dfrac{7}{8}\neq 9.$

So, this option is not correct.

Option (B) :  Here, the given function is

$y=\left(\dfrac{1}{2}\right)^{x-3}+1.$

So, at x = 0, the value of y is given by

$y(x=0)=\left(\dfrac{1}{2}\right)^{0-3}+1=\left(\dfrac{1}{8}\right)^{-1}+1=8+1=9.$

So, this option is CORRECT.

Option (C) :  Here, the given function is

$y=\left(\dfrac{1}{2}\right)^{x-1}+3.$

So, at x = 0, the value of y is given by

$y(x=0)=\left(\dfrac{1}{2}\right)^{0-1}+3=2+3=5\neq 9.$

So, this option is not correct.

Option (D) :  Here, the given function is

$y=\left(\dfrac{1}{2}\right)^{x+1}-3.$

So, at x = 0, the value of y is given by

$y(x=0)=\left(\dfrac{1}{2}\right)^{0+1}-3=\dfrac{1}{2}-3=-\dfrac{5}{2}\neq 9.$

So, this option is not correct.

Thus, (B) is the correct option.