Polynomial Functions
The degree of the polynomial function f(x) = 3x^4 - 2x^2 + 5x - 1
What is the fourth degree?
Find the x-intercepts of the Rational Function f(x) = x^2 -4 / x - 2
X-intercepts: (-2, 0) and (0, 2)
-2log4(x-5)=1. Find x
x=11/2
Consider the equation of a parabola: y = x^2 + 2x - 3. Find the limit of y as x approaches 2. Show your work.
at x = 2, y = 5
The sum of the coefficients in the polynomial function g(x) = 2x^3 - 5x^2 + 3x + 1
What is 1?
Find the vertical asymptotes of the Rational Function f(x) = 3x + 1 / x^2 + 4x - 5
Vertical Asymptotes: x = 1 and x = -5
f(x)= 3^(2x). Find y when x=4
y=6561
(x - 2)^2/16 + (y + 3)^2/9 = 1. Find the limit of y as x approaches 2 from the right side. Show your work.
the limit of y as x approaches 2 from the right side is 0.
The x-intercept of the polynomial function f(x) = -2x^3 + 3x^2 - 4x + 1
What are the x-intercepts (-1, 0), (1, 0), and (0.5, 0)?
Find the x and y intercepts as well as the asymptotes for this Rational Function --> f(x) = -4/ x-2
y-int: (0,2) or y=2
x-int: (2,0) or x=2
Vertical Asymptote: x=2
No Horizontal Asymptote
F(x)=log2(2x+3) Find 3 points on this graph
(1, 2.322)
(2,2.807)
(3,3.17)
(x - 1)^2/4 - (y - 2)^2/9 = 1. Find the limit of y as x approaches 1. Show your work.
There are no real solutions.
The polynomial function g(x) = 4x^3 - 2x^2 + 3x - 1, find the y-coordinate when x = 2
What is 29?
Find the x -int, y-int, Asymptotes, Domain, and Range of this Rational Function f(x) = x^2 - 25 / x + 1
Slant Asymptote: y = x - 1
Vertical Asymptote: x = -1
x-int: x = 5, x = -5
y-int: y = -25
f(x)=log2(x^2+5x+1) = 5. Find x
-5 + sqrt149/2
5-sqrt149/2
y = x^2 - 4x + 3. Determine the coordinates of the vertex and the equation of the axis of symmetry. Show your work.
vertex: (2, -1)
Axis of symmetry: x=2
The polynomial function f(x) = 2x^4 - 5x^3 + 3x^2 + 2x - 1, find the y-coordinate when x = -1
What is -3?
Find the both x and y intercepts, asymptotes, Domain and Range, when f(x) > 0 and f(x) < 0, as well as when f(x) both increase and decreases for the Rational Function f(x) = x + 5 / x^2 + 6x + 5
Horizontal Asymptote: y = 0
Vertical Asymptote: x = -1
x-int: x = -5
y-int: y = 1
D: (-infinity, -5), (-5, -1), (-1, +infinity)
R: (-infinity, 1), (1, +infinity)
f(x) > 0: (-1, +infinity)
f(x) < 0: (-infinity, -5), (-5, -1)
No increase
Decrease: (-infinity, -5), (-5, -1), (-1, infinity)
f(x)=3^(2x+1)-5 = 8. Find x
1/2log3(13)-1/2
9(x - 1)^2 + 4(y + 2)^2 = 36. Determine the center, major axis length, and minor axis length of the ellipse. Show your work.
major axis length = 1.
minor axis length = 2/3.
center of the ellipse = (1, -2)
Work:
9(x - 1)^2 + 4(y + 2)^2 = 36
(x - 1)^2/4 + (y + 2)^2/9 = 1
(h, k) = (1, -2).
(x - 1)^2 is 4 => 2a = 2√(1/4) = 1.
(y + 2)^2 is 9 => 2b = 2√(1/9) = 2/3.