Which of the following options represents the graph of the function shown below? ƒ(x) = (x - 3)^3 1 1 ƒ(x) = (x - 3)^3 + 1 ƒ(x) = (x + 3)^3 - 1 ƒ(x) = (x + 3)^3 + 1

Question

asked Mar 22, 2018 219k views

2 Answers

Natu · Answer 1 · 2018-03-28T16:24:22+0000

The function that best represents the graph of the function which is given is:

f(x)=(x-3)^2+1

From the graph that is provided to us we observe that the graph passes through the point (3,1).

Hence, we will check which of the following function satisfies this point.

a)

f(x)=(x-3)^3-1

when x=3 we see that:

$f(x)=(3-3)^3-1\\\\i.e.\\\\f(x)=-1\\eq 1$

Hence, option: a is incorrect.

c)

f(x)=(x+3)^3-1

when x=3 we have:

$f(3)=(3+3)^3-1\\\\i.e.\\\\f(3)=9^3-1\\\\i.e.\\\\f(3)=729-1\\\\f(3)=728\\eq 1$

Hence, option: c is incorrect.

d)

f(x)=(x+3)^3+1

when x=3 we have:

$f(3)=(3+3)^3+1\\\\i.e.\\\\f(3)=9^3+1\\\\i.e.\\\\f(3)=729+1\\\\f(3)=730\\eq 1$

Hence, option: d is incorrect.

Now we are left with option: b)

i.e.

b)

f(x)=(x-3)^2+1

Also, when x=3 we have:

$f(3)=(3-3)^2+1\\\\f(3)=0+1\\\\f(3)=1$

Hence, it passes through the point (3,1)

Also, when we will plot this function we observe that it matches the given graph.