f(x) > 0
f(x) < 0
f(x) = 0
End Behavior
IVT
100
Given the function sign chart, state where f(x) > 0.
f(x) > 0 on the interval (-5, 0) U (0, 1)
100
Given the function sign chart, state where f(x) < 0.
f(x) < 0 on the interval
(-oo, -3)U(1,7)
100
Given the function sign chart, state where f(x) = 0.
f(x) = 0 at x = -6, x = 0, x = 1, and x = 7
100
State the end behavior of the function below:
f(x)=5.3x^4+7x+1
x->-oo, f(x)->+oo
x->+oo,f(x)->+oo
100
What does IVT stand for?
Intermediate Value Theorem
200
State where f(x) > 0
f(x)=-x^2(x-3)(x+1)
f(x) > 0 on the interval (-1, 0)U(0,3)
200
State where f(x) < 0.
f(x)=(x+3)(x-4)(x+1)^2
f(x) < 0 on the interval (-3, -1) U (-1, 4)
200
State where f(x) = 0
f(x)=-2x(x-3)(x+4)
f(x) = 0 at x = 0, x = 3, and x = -4
200
State the end behavior of the function below:
g(x)=-1/2x^2+5
x->-oo,g(x)->-oo
x->+oo,g(x)->-oo
200
The function must have at least one zero on the interval(s):
(-2, -1); zeros at x = 3 and x = 5.
300
State where the function is positive.
f(x)=-2(x-4)(x+2)
The function is positive on the interval (-2,4).
300
State where the function is negative.
f(x)=(3-x)(x+1)(x-1)
The function is negative on the interval
(-1,1)U(3,+oo)
300
State the zeros of the function. Include multiplicity.
f(x)=x(3-x)(5-x)^2
The zeros of the function are at x = 0, x = 3, and x = 5 (multiplicity of 2).
300
State the end behavior of the function
f(x)=-x^2(3-x)(x+5)^2
x->-oo, f(x)->-oo
x->+oo,f(x)->+oo
300
The function must have at least one zero on the interval(s):
(1, 2), (3, 4), (6, 7). Zeros at x = -1
400
State where the value of f(x) is positive.
f(x)=x^3+4x^2-x-4
f(x) is positive on the interval
(-4,-1)U(1,+oo)
400
State where the value of f(x) is negative.
f(x)=x^5+5x^4+6x^3
f(x) is negative on the interval
(-oo,-3)U(-2,0)
400
State the x-intercepts of the function.
f(x)=x^3+3x^2+4x+12
The x-intercepts of the function are at x = -3
400
State the end behavior of the function.
g(x)=-x(x+1)^2(5+x)^2
x->-oo, g(x)->+oo
x->+oo,g(x)->-oo
400
Given the table, f(x) has to have at least how many zeros?
At least 4 zeros
500
State where f(x) > 0.
f(x)=-x^4-x^3+12x^2
f(x) > 0 on the interval (-4, 0) U (0, 3)
500
State where f(x) < 0.
f(x)=-x^3+x^2+4x-4
f(x) < 0 on the interval
(-2,1)U(2,oo)
500
State the roots of the function.
f(x)=x^4-64x
The roots of the function are at x = 0 and x = 4
500
State the end behavior of the function
f(x)=(2x-5)(x-2)(x^2+1)(4-x)^2
x->-oo,f(x)->+oo
x->+oo,f(x)->+oo
500
The function must have at least one zero on the interval(s):
(0, 1) and (3, 4). Zeros at x = -2