Question

QUESTION 11:

Consider the graphed function. Based on its end behavior, which of the following could be its equation? (photo attached below):
A) f (x)= x^3 + 6x^2-5x
B) f (x)= -x^4 +6x^3 - 5x^2
C) f (x)= x^4 +6x^3-5x^2
D) f (x)= -x^3+ 6x^2-5x

QUESTION 12:
Divide x2 by x – 1. What is the value of the remainder?
A) 0
B) 1
C) -1
D) 2

Answer 1

A is the right answer

Answer 2

Based on the end behavior, the equation graphed is

• D) f (x)= -x^3+ 6x^2-5x

Dividing x² by x – 1 will have a remainder of

B) 1

What is end behavior

End behavior refers to the behavior or trend of the graph of a function as the input values (x) approach positive or negative infinity.

for odd-degree polynomials, the end behavior is determined by the sign of the leading coefficient. If the leading coefficient is positive, the polynomial rises on the right and falls on the left. If the leading coefficient is negative, the polynomial falls on the right and rises on the left.

In the case of the graph we can see that the leading coefficient is negative.

QUESTION 12:

The remainder theorem states that if you divide a polynomial (f(x)) by a linear factor of the form (x - c), then the remainder is (f(c)).

In this case, (f(x) = x²) and (c = 1) (since (x - 1) is the divisor). So, substitute (x = 1) into (f(x) = x²)

f(1) = 1² = 1

hence, the remainder when dividing (x²) by (x - 1) is 1.