Consider the polynomial function p(x)= -9x^9 +6x^6 -3x^3 +1.
2 answers:
Answer:
The end behavior of the graph of p is:
f(x) → ∞ as x → -∞ and f(x) → -∞ as x → ∞
Step-by-step explanation:
Given the polynomial function
Since the leading term of the polynomial (the term in a polynomial that contains the highest power of the variable) is -9x⁹, then the degree is 9 i.e. odd, and the leading coefficient is -9, i.e. negative.
This means that f(x) → ∞ as x → -∞ and f(x) → -∞ as x → ∞
The graph is also attached below.
Thus, the end behavior of the graph of p is:
f(x) → ∞ as x → -∞ and f(x) → -∞ as x → ∞
You might be interested in
The line g(x) has slope ...
(change in y)/(change in x) = (-18 -(-20))/(1 - 0) = 2
so can be written in slope-intercept form as
g(x) = 2x -20
The x-intercept of this line is at x=10.
0 = 2x -20 . . . . the x-intercept is where g(x) = 0
20 = 2x
10 = x
The circle also intersects the x-axis at x=10, so that will be one point that is shared by the circle and g(x). A graph shows there is also another point of intersection, (6, -8).
Yes, the linear function g(x) will intersect the circle at 2 points with positive x-coordinates.
(change in y)/(change in x) = (-18 -(-20))/(1 - 0) = 2
so can be written in slope-intercept form as
g(x) = 2x -20
The x-intercept of this line is at x=10.
0 = 2x -20 . . . . the x-intercept is where g(x) = 0
20 = 2x
10 = x
The circle also intersects the x-axis at x=10, so that will be one point that is shared by the circle and g(x). A graph shows there is also another point of intersection, (6, -8).
Yes, the linear function g(x) will intersect the circle at 2 points with positive x-coordinates.