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

graph of function g of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 8 and 5, 32 and 6, 64. Graph of function f of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 10 and 5, 26 and 6, 37

f(x), because an increasing quadratic function will eventually exceed an increasing exponential function
g(x), because an increasing exponential function will eventually exceed an increasing quadratic function
f(x), because an increasing exponential function will always exceeds an increasing quadratic function until their graphs intersect
g(x), because an increasing quadratic function will always exceeds an increasing exponential function until their graphs intersect

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flightbath flightbath · Answer 1 · 2019-01-17T12:21:09+01:00

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 [tex]g(x)=2^x[/tex] 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:

[tex]ax^2+bx+c=y[/tex]

Taking (0,1)

[tex]a(0)+b(0)+c=1[/tex]

c=1

Now, taking (1,2)

[tex]a+b+1=2[/tex]

[tex]a+b=1[/tex] (1)

Now, taking (3,10)

[tex]a(3)^2+b(3)+1=10[/tex]

[tex]9a+3b=9[/tex] (2)

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

a=1 and b=0

Hence, the function [tex]f(x)=x^2+1[/tex]

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.