Question

If `f(x)` is an even function passing through `(2,5)` then what other point must it pass through?

Answer 1

If `f(x)` is an even function including the point `(2, 5)` then it will also include the point `(-2, 5)`...

Explanation:

• To say that `f(x)` is an even function is to say that for any `x` in its domain `f(-x) = f(x)`.

• To say that `(2, 5)` is a point on the graph of `f(x)` is to say that `f(2) = 5`.

Hence we can deduce that `f(-2) = 5` and `(-2, 5)` is also a point on the graph of `f(x)`.