If f and t are both even functions, is the product ft even? if f and t are both odd functions, is ft odd? what if f is even and t is odd? justify your answers.

(a) If f and t are both even functions, product ft is even.

(b) If f and t are both odd functions, product ft is even.

(c) If f is even and t is odd, product ft is odd.

Step-by-step explanation:

Even function: A function g(x) is called an even function if

Odd function: A function g(x) is called an odd function if

(a)

Let f and t are both even functions, then

The product of both functions is

The function ft is even function.

(b)

Let f and t are both odd functions, then

The product of both functions is

The function ft is even function.

(c)

Let f is even and t odd function, then

The product of both functions is

The function ft is odd function.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this