Characteristics of Functions
What is the domain of the function f(x)=1 / X - 2 ?
X does not equal 2
What is the remainder when f(x)=x^3−3x+2 is divided by x−1?
0
What is the degree of the polynomial f(x)=3x^5−4x^3+2x^2−7 ?
5
Solve the inequality x+3>5.
x>2
Find the intervals where f(x)=x^3−4x < 0.
(−∞,−2)∪(0,2)
Identify the range of the function f(x)= *roor of* x−3
y greater than or equal to 0
Use the factor theorem to determine if x−2 is a factor of f(x)=x^3−4x^2+x+6
Yes
Determine the leading coefficient of f(x)=−2x^4+3x^3−x+5
-2
Solve the inequality 2x−1≤3.
x≤2
Find the intervals where f(x)=x^4−5x^2+4 > 0
(−∞,−2)∪(−1,1)∪(2,∞)
For the function f(x) =x^2−4x+4, find the vertex.
(2,0)
Find the remainder when f(x)=2x^4−3x^3+5x−8 is divided by x+1.
-8
Write the polynomial function with roots 2,−1 and 3.
f(x)=(x−2)(x+1)(x−3)
Solve the quadratic inequality x^2−4x−5>0
x<−1 or x>5
Find the intervals where f(x)=x^5−5x^3+4x ≥ 0.
[-2,-1]∪[0,1]∪[2,∞)
Determine whether the function f(x)=x^3−3x^2+2 is even, odd, or neither.
neither
Given that (x+3) is a factor of f(x)=x^4+2x^3−9x^2−2x+15, find another factor.
x - 1
Given f(x)=x^3−3x^2−4x+12, find the x-intercepts.
x=−2,2,3
Solve the inequality x+2/x−1≥0.
x≤−2 or x>1
Find the intervals where f(x)=x^5−3x^4+2x^3< 0.
(−∞,0]∪[1,2]
Identify the intervals on which the function f(x)=x^4−4x^2 is increasing.
(−∞,−1)∪(1,∞)
If f(x)=x^4−6x^3+11x^2−6x, use the factor theorem to factor f(x) completely.
f(x)=(x−1)2(x−2)(x−3)
If P(x)=x^4+6x^3+11x^2+6x, express P(x) in factored form.
P(x)=(x+1)(x+1)(x+2)(x+3)
Solve the inequality (x−2)(x+3)≤0
−3≤x≤2
Find the intervals where f(x)=x^4−4x^3+4x^2 ≤ 0.
[0,2]