#1**+3 **

f(x) = x^{6}

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} = 1^{6} = 1

f(-1) = (-1)^{6} = 1^{6} = 1

and

f(2) = (2)^{6} = 2^{6} = 64

f(-2) = (-2)^{6} = 2^{6} = 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

#1**+3 **

Best Answer

f(x) = x^{6}

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} = 1^{6} = 1

f(-1) = (-1)^{6} = 1^{6} = 1

and

f(2) = (2)^{6} = 2^{6} = 64

f(-2) = (-2)^{6} = 2^{6} = 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