Question

If F(x) = 2 - xand w(x) = x - 2, what is the range of (w•p(x)?

0 (-0,0)
0 (-0,2]
0 (0,00)
[2.00)

Answer 1

Th Range is [0, -∞)

Explanation:

f(x) = 2 - x

w(x) = x - 2

We want to find the range of (f * w)(x).

First, we need to find (f * w)(x), which is the multiplication of the function f(x) and the function w(x). Lets use algebra to find (f * w)(x):

`(f*w)(x)=(2-x)(x-2)\\=2x-4-x^2+2x\\=-x^2+4x-4`

This is a quadratic function (U shaped), or a parabola. The graph is attached.

The range is the set of y-values for which the function is defined.

We see from the graph that the parabola is upside down and the highest value is y = 0 and lowest goes towards negative infinity. So the range is from 0 to negative infinity. Or,

0 < y < ∞

In interval notation, that would be:

[0, -∞)