Part 1
The graph has even symmetry. You can see that because it is symmetric with respect to the y-axis.
Functions that have even symmetry have the following property:
Part 2
To answer this we can simply check if the property we mentioned earlier holds for this function.
We can see that sine does not have even symmetry.
In fact, sine function has the following property:
This is called odd symetry.
Part 3
Take a look at the function that you attached in the picture. We know that function has even symmetry.
Reflection over x-axis and <span>180° rotation around the origin would give us -f(x). We would not end up with the same function, so these two are out.
</span><span>90° rotation around the origin would mean we swapped x <span>and y</span> so that one is out too. R</span><span>eflection over the line y=x is a property of functions that have an odd symmetry.
We are left with reflection around y-axis and, as mentioned before, this is the property of evenly symmetric functions.</span>
The graph has even symmetry. You can see that because it is symmetric with respect to the y-axis.
Functions that have even symmetry have the following property:
Part 2
To answer this we can simply check if the property we mentioned earlier holds for this function.
We can see that sine does not have even symmetry.
In fact, sine function has the following property:
This is called odd symetry.
Part 3
Take a look at the function that you attached in the picture. We know that function has even symmetry.
Reflection over x-axis and <span>180° rotation around the origin would give us -f(x). We would not end up with the same function, so these two are out.
</span><span>90° rotation around the origin would mean we swapped x <span>and y</span> so that one is out too. R</span><span>eflection over the line y=x is a property of functions that have an odd symmetry.
We are left with reflection around y-axis and, as mentioned before, this is the property of evenly symmetric functions.</span>