Show:
Point of Dis/Continuity
Zeros
End Behavior
Extrema
Function Composition
100
The function is f(x) = (x+4) / (x^2 -16). Is the point continuous at x=0? If not, what is type of discontinuity?
Yes, x=0 is a point of continuity.
100
Determine which consecutive integers the real zeros of each function. f(x) = 2x -3 at [-4,4]
zeros between 1&2
100
End behavior describes the behavior at the ends of the ___-axis.
x-axis
100
Use the function to estimate the intervals on which the function is increasing decreasing, or constant. f(x)=-6
constant behavior (-∞,∞)
100
given f(x)=x^2+4x, g(x)=x+2, and h(x)= 3x-5 Find (f+g)(x)
(f+g)(x) = x^2 +5x + 2
200
The function is f(x) = (x+4) / (x^2 -16). Is the point continuous at x=4? If not, what is type of discontinuity?
No, x=4 is a point of removable discontinuity.
200
Determine which consecutive integers the real zeros of each function. f(x) = x^3 - 9x + 2 at [-4,4]
zeros between -1&0 and 0&1
200
How would you write the statement using math symbols "the limit of f(x) as x approaches negative is infinity."
SEE BOARD
200
Use the function to estimate the intervals on which the function is increasing decreasing, or constant. f(x)=-2x^3
decreasing behavior (-∞,∞)
200
given f(x)=x^2+4x, g(x)=x+2, and h(x)= 3x-5 Find (g - h)(x)
(g - h)(x) = -2x + 7
300
The function is f(x) = (x+4) / (x^2 -16). Is the point continuous at x=-4? If not, what is type of discontinuity?
No, x=-4 is a point of infinity discontinuity.
300
Determine which consecutive integers the real zeros of each function. f(x)= x^3 - 9x + 2 at [-5,5]
zeros between -4&-3, 0&1 and 2&3
300
Use the function of f(x)= -x^3-4x^2+2 to describe its end behavior.
the limit of f(x) as x approaches - infinity = infinity the limit of f(x) as x approaches infinity = - infinity
300
Locate and classify maximums and minimums. f(x)= x^3 - 9x + 2
relative maximum (-1.7, 12.4) relative minimum (1.7, -8.4)
300
given f(x)=x^2+4x, g(x)=x+2, and h(x)= 3x-5 Find (fg)(x)
(fg)(x) = x^3 + 6x^2 + 8x
400
The function is f(x) = x^2 + 6x + 5. Is the point continuous at x=0? If not, what is type of discontinuity?
Yes, x=0 is a point of continuity.
400
Determine which consecutive integers the real zeros of each function. f(x)= -2x^3 + 5x - 1 at [-5,1]
zeros between -2&-1 and 0&1; 1&2 are not included in the given interval
400
Use the function of f(x)= - abs(x+1) to describe its end behavior.
the limit of f(x) as x approaches - infinity = - infinity the limit of f(x) as x approaches infinity = - infinity
400
Locate and classify maximums and minimums. f(x)= x^5 - 2x^4 - 2x^3 + 3x^2
Relative minimums (0, 0), (1.9, -4.2) Relative maximums (-1.0, 2.0), (.7, .5)
400
given f(x)=x^2+4x, g(x)=x+2, and h(x)= 3x-5 Find (h o g) (x)
(h o g) (x)= 3x +10
500
What is the interval in which the function, f(x) = (x+4) / (x^2 -16), exists.
(-infinity, -4) U (-4,4) U (4, infinity)
500
You have 20seconds to name the theorem that states: "If f(x) is a continuous function, and f(a) and f(b) have opposite signs, then there exists at least one value c, such that a
The Location Pronciple
500
Use the function of f(x)= 1 / (x - 4) - 3 to describe its end behavior.
the limit of f(x) as x approaches - infinity = -3 the limit of f(x) as x approaches infinity = -3
500
Locate and classify maximums and minimums. f(x)= -0.5x^4 + 2.5x^3 + x^2 - 6.5
relative maximum (-0.9, 4.5) relative minimum (0.9, -3.5) absolute maximum (3.8, 22.7)
500
given f(x)=x^2+4x, g(x)=x+2, and h(x)= 3x-5 Find (fgh)(x)
(fgh)(x) = 3x^4 + 13x^3 - 6x^2 - 40x