Which of the following equations demonstrate that the set of polynomials is not closed under the certain operations?
a. division: (x^2+2x) / (x+1) = x+ x/x+1
b. multip.: (3x^4++x^3)= -6x^6+ x^7+x^6
c. addition: (3x^4+x^3)+(-2x^4+x^3)= x^4 + 2x^3
d. multip.: (x^2+2x)(x+1)= x^3 +3x^2+2x

Solution:

A. Division

→→→True

B. Multiplication

L HS

R HS

LHS ≠ RHS

→→→→False

C: Addition

L HS

→→→True

D: Multiplication

LHS

→→→True

Option B: is not correctly closed under Multiplication.

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation:

5x + 5

step-by-step explanation:

you should always add the diagrams and graphs we cannot see. this particular question is kind of borderline because we can make a graph for you.

(f + g)x = -x^2 +3x + 5 + x^2 + 2x

(f + g)x = 5x + 5

the graph of z = 5x + 5 is shown below. always use desmos when in doubt.