AP Precalc / Symmetry & Inverses / 9.17.24

When you reflect over the x-axis, (x, y) becomes...

(x, -y)

When you reflect over the y-axis, (x, y) becomes...

(-x, y)

When you reflect over the origin, (x, y) becomes...

(-x, -y)

When you reflect over the line y = x, (x, y) becomes...

(y, x)

Is a cosine function even or odd?

Even

Is a sine function even or odd?

Odd

Is an identity function (y = x) even or odd?

Odd

How do you confirm if a function is an inverse of another function?

If (f ∘ f^-1)(x) = x, these two are inverses.

When a function is even, it’s always symmetric about the…

y-axis

When a function is odd, it’s always symmetric about the…

origin

How do you determine if a function is even?

If f(x) = f(-x)

How do you determine if a function is odd?

If f(-x) = -f(x)

What line is any quadratic function ax² + bx + c symmetric about?

The vertical line x = -b/2a

How do you determine if f(x) and g(x) are inverses of each other?

If f(g(x)) = x and g(f(x)) = x.