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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)

User Mog
by
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1 Answer

4 votes

Answer:

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, -∞)

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)-example-1
User Symeon Mattes
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