Polynomial Functions
What is the degree of the polynomial: f(x)=−2x^4+x^2−7
degree 4
What is the vertical asymptote of f(x)=1/x−4
4
Solve: log2 base 2 (8)
3
What is the period of sin(x)
2 pi
What does f(x)+3 do to a function
vertical shift up 3 units
Identify the end behaviour of f(x)=3x^5−2x+6
as x approaches (-)infinity ,f(x) approaches (-) infinity
as x approaches (+)infinity ,f(x) approaches (+) infinity
Odd degree, positive leading coefficient.
Find the horizontal asymptote of f(x)=2x^2+3/4x^2−1
y=2/4 which = 1/2
Write 3 to the power of x =81 in logarithmic form and solve.
x=log base 3 (81)=4
1/2
What does f(x-2) do?
Horizontal shift right 2 units
Factor completely: x^3−3x^2−4x+12
(x-3)(x+2)(x-2)
Determine the x-intercepts of f(x)=x^2−9/x+3
x=3
Expand: log(x^3/root y)
3log(x)-1/2 log (y)
Solve: sin(x) = root 3/ 2
on [0,2pi]
x= pi/3, 2pi/3
if f(x)=x^2 what is the effect of -f(x)
Reflect over x axis
Use long division to divide: (2x^3+x^2−5x+4)÷(x−1)
2x^2+3x-2
remainder 2
Identify any holes in the function: f(x)=x^2−1/x−1
x=1
Solve: log base 5 (x+1)=2
x+1=25 so x=24
Graph y=2sin (3x- pi)+1
state amp and phase shift
amp=2, phase shift= pi/3, vertical shift=1
Describe the transformation of y=−2 rootx+1 +4
Reflect over x-axis, vertical stretch by 2, left 1, up 4
A polynomial function has degree 4 and leading coefficient 1. It has a double root at x=2,a root at x=−1, and its y-intercept is 8.
Find the equation of the polynomial in standard form.
f(x)=(x−2)^2(x+1)(x+2)
Solve: 2x+1/x−3=1
x=-4
Solve: 3^x+1=4 ^x−2
Give answer as decimal rounded to the 10th
-13.45
Prove the identity 1+tan^2 x =sec^2 x
Self guided
(I can't put full answer due to word cap)
Given f(x)=x^2, find the equation for a vertical compression by 1/2 and a reflection in the y-axis.
f(x)=1/2(-x)^2= 1/2x^2