Question

A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function?

Answer 1

Answer:

Option 2 is correct.

Step-by-step explanation:

We have been given points of g(x) and f(x)

g(x)  has ordered pairs  (0,1) ,(1,2) ,(3,8) ,(5,32) and (6,64) this is an exponential function which is $g(x)=2^x$ from the given points.

f(x) has ordered pairs (0,1) ,(1,2) ,(3,10) ,(5,26) and (6,37)  this is a quadratic function

We will put these values in the quadratic function which is:

$ax^2+bx+c=y$

Taking (0,1)

$a(0)+b(0)+c=1$

c=1

Now, taking (1,2)

$a+b+1=2$

$a+b=1$   (1)

Now, taking (3,10)

$a(3)^2+b(3)+1=10$

$9a+3b=9$      (2)

Now, solving the equation (1) and (2) we get:

a=1 and b=0

Hence, the function $f(x)=x^2+1$  

Please look at the attachment for the graph

We can see that the g(x) an exponential function will eventually exceed the increasing quadratic function

Therefore, option 2 is correct.