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# ​ Which graph represents f(x)=x6 ?

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Which graph represents  f(x)=x6 ?

Feb 7, 2018

#1
+8963
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f(x)   =   x6

Notice that a negative number raised to an even power is the same as the positive version of the number raised to the power. For example...

f(1)   =   (1)6   =   16   =   1

f(-1)   =   (-1)6   =   16   =   1

and

f(2)   =   (2)6   =   26   =   64

f(-2)   =   (-2)6   =   26   =   64

This is true for all numbers and their negatives. This makes the graph symmetrical about the y-axis.

We can rule out the second and fourth option because on those graphs, for example,  f(1)  ≠  f(-1)

We just found that  f(2)  =  64 , so the graph of  f(x)  should pass through the point  (2, 64) .

The first graph passes through the point  (2, 4) , so it can't be right.

The correct graph must be the third one.

Feb 8, 2018

#1
+8963
+3

f(x)   =   x6

Notice that a negative number raised to an even power is the same as the positive version of the number raised to the power. For example...

f(1)   =   (1)6   =   16   =   1

f(-1)   =   (-1)6   =   16   =   1

and

f(2)   =   (2)6   =   26   =   64

f(-2)   =   (-2)6   =   26   =   64

This is true for all numbers and their negatives. This makes the graph symmetrical about the y-axis.

We can rule out the second and fourth option because on those graphs, for example,  f(1)  ≠  f(-1)

We just found that  f(2)  =  64 , so the graph of  f(x)  should pass through the point  (2, 64) .

The first graph passes through the point  (2, 4) , so it can't be right.

The correct graph must be the third one.

hectictar Feb 8, 2018