Determine the end behavior of the graph of the function fx

Determine the end behavior of the graph of the function. f(x) = -5x^5+9x^4-2x^3+2 Up left and up right Down left and up right Down left and down right Up left and down right Find the zeros of the function and state the multiplicities. f(x) =-4x^3 (x + 1)^3(x - 5)^6 0 (multiplicity 3), -1 (multiplicity 4),5 (multiplicity 6) -1 (multiplicity 4), 5 (multiplicity 6) 0 (multiplicity 3), 1 (multiplicity 4), -5 (multiplicity 6) 1 (multiplicity 4), -5 (multiplicity 6)

Solution

4. the correct answer is option D) up left and down right

when x is negative say -x then f(-x)=-5(-x)^5+9(-x)^4-2(-x)^3+2=5x^5+9x^4+2x^3+2>0   always a positive quantity

hence it is up on the left

when x is very high positive then x^5 is very dominant and it has a negative coefficient hence f(x) is a negative quantity when x is very high positive.

hence it is down on right

5. the answer is option A) 0(multiciplicity 3),-1(multiciplity 4),5(multiciplity 6)

since f(x)=-4x^3(x+1)^4(x-5)^6   hence the roots are 0 -1 and 5

now x has power 3 hence 0\'s multiciplity is 3     (x+1) has power 4 hence -1\'s multiciplity is 4     (x-5) has power 6 hence 5\'s multiciplity is 6