Question

If f(x) is a even function and (6,8) is one the points on the graph of f(x), what explains why (-6,8) must also be a point on the graph?

Answer 1

an even function can be reflected across the y axis and remain the same
for an even function, if (a,b) is a point, (-a,b) is also a point on that line

Answer 2

Symmetry about y-axis

Explanation:

If f(x) is a even function and (6,8) is one the points on the graph of f(x).

Even Function: It makes symmetry about y-axis. The value of y is same from origin to left side and right side of y-axis.

Even function:

`f(x)=f(-x)`

For even function, if (6,8) point on f(x) then (-6,8) must be on f(x).

`f(6)=f(-6)=8`

The value of y=8 is same 6 unit from left and right of y-axis 6.

Both points are on function because it is symmetry about y-axis for even function.