Question

1) Name the property of real numbers illustrated by the equation. -4(x+4)=-4x-16

A.associative property of addition
B.commutative property of addition
C.associative property of multiplication
D.distributive property
2) Given no other restrictions what are the domain and range of the following function?
F(x)=x^2-2x+1
A. D=all real numbers
R=all real numbers
B. D=all real numbers
R={yI>_ -1
C. D=all real numbers
R={yIy>_0}
D. D{xIx>_0}
R={yIy<_1}

Answer 1

1) D. distributive property

2) C. D=all real numbers; R = y ≥ 0

Explanation:

1) We observe that the factor of -4 has been multiplied by each of the terms of the binomial in parentheses. This is an application of the distributive property.

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2) Any polynomial has a domain of all real numbers. The range of an even-degree polynomial will be limited by its extreme value. Here, the vertex of this quadratic function is (1, 0), so the range is all non-negative real numbers.

F(x) = x^2 -2x +1 = (x -1)^2

Any square will have a minimum value of 0. For this function, that occurs at ...

(x, y) = (1, 0)

The range will be values of y equal to or greater than zero.