Which of the following polynomials could have the same end behavior as f(x)=ax^6+bx^5+c?
There may be more than one correct answer. Select all correct answers.
a. nx^5+bx^4+c
b. kx+b
c. dx^4−bx^3−cx^2+dx+e
d. −jx^8+bx^7+cx^4
e. −mx^2
can someone help me with this it is confusing and there is more than one answer so yea i need help
ax^6 has a range that tends towards positive infinity.
Any function that has a +2, 4,6,8 as the power, and has a leading numerical coefficient that is POSITIVE has a range that tends towards positive infinity...
Does that help ??
it sort of makes sense could you explain it a little further
If the power is EVEN the ends of the graph go upwards towards the sky! Both arms of the function go upwards.
that is 2x^2, 4^6, 1x^8 etc all have leading coefficients that are positive so the graphs go upwards.
if the function was y = - x^2 then the graph would go downwards (in quadrants 3 and 4).
You may wish to use www.desmos to graph your functions so you can see what I am describing : )
To determine which polynomials could have the same end behavior as f(x) = ax^6 + bx^5 + c, we need to focus on the highest degree terms of the polynomials. The end behavior of a polynomial is determined by the sign of the coefficient of the highest degree term.
In this case, the highest degree term is ax^6. Here are the possible options:
a. nx^5 + bx^4 + c: This is a polynomial of degree 5. Since the highest degree term is nx^5, it is not possible for this polynomial to have the same end behavior as f(x).
b. kx + b: This is a polynomial of degree 1. Since the highest degree term is kx, it is not possible for this polynomial to have the same end behavior as f(x).
c. dx^4 - bx^3 - cx^2 + dx + e: This is a polynomial of degree 4. Since the highest degree term is dx^4, it is not possible for this polynomial to have the same end behavior as f(x).
d. -jx^8 + bx^7 + cx^4: This is a polynomial of degree 8. Since the highest degree term is -jx^8, it is possible for this polynomial to have the same end behavior as f(x). The negative sign does not affect the end behavior.
e. -mx^2: This is a polynomial of degree 2. Since the highest degree term is -mx^2, it is possible for this polynomial to have the same end behavior as f(x). The negative sign does not affect the end behavior.
In summary, the polynomials that could have the same end behavior as f(x) = ax^6 + bx^5 + c are d. -jx^8 + bx^7 + cx^4 and e. -mx^2.