Question

**f(x) = x3 – 3x2 + 10** Domain:
________________________________ Range:
________________________________ x-int: ______________ y-int:
______________ Maxima: _______________________________ Minima:
________________________________ Increasing:
_____________________________ Decreasing:
_____________________________ Constant:
______________________________ End Behavior:
___________________________ Discontinuities:
__________________________ Asymptote: _____________________________
Symmetry: _____________________________Graph:

**f(t) = 2t4 – 10t2 + 12.5t** Domain:
________________________________ : Range:
________________________________ x-int: ______________ y-int:
______________ Maxima: _______________________________ Minima:
________________________________ Increasing:
_____________________________ Decreasing:
_____________________________ Constant:
______________________________ End Behavior:
___________________________ Discontinuities:
__________________________ Asymptote: _____________________________
Symmetry: _____________________________Graph:

**f(x) = 2x4 – 6x2 + 4.5** Domain:
________________________________ : Range:
________________________________ x-int: ______________ y-int:
______________ Maxima: _______________________________ Minima:
________________________________ Increasing:
_____________________________ Decreasing:
_____________________________ Constant:
______________________________ End Behavior:
___________________________ Discontinuities:
__________________________ Asymptote: _____________________________
Symmetry: _____________________________Graph:

**f(t) = 2t5 + 4t3 – 11t2 + 6** Domain:
________________________________ : Range:
________________________________ x-int: ______________ y-int:
______________ Maxima: _______________________________ Minima:
________________________________ Increasing:
_____________________________ Decreasing:
_____________________________ Constant:
______________________________ End Behavior:
___________________________ Discontinuities:
__________________________ Asymptote: _____________________________
Symmetry: _____________________________Graph:

Answer #1

Increaing, decreasing values and end behaviours as in below table:

??<x<0 | |||||

f(x) = 3x + 2
Domain:
________________________________
Graph:
Range: ________________________________
x-int: ______________ y-int: ______________
Maxima: _______________________________
Minima:
________________________________
Increasing: _____________________________
Decreasing: _____________________________
Constant: ______________________________
End Behavior: ___________________________
Discontinuities: __________________________
Asymptote: _____________________________
Symmetry: _____________________________
f(x) = ½ x – 4
Domain:
________________________________
Graph:
Range: ________________________________
x-int: ______________ y-int: ______________
Maxima: _______________________________
Minima:
________________________________
Increasing: _____________________________
Decreasing: _____________________________
Constant: ______________________________
End Behavior: ___________________________
Discontinuities: __________________________
Asymptote: _____________________________
Symmetry: _____________________________
f(x) = x2 + x + 6
Domain:
________________________________
Graph:...

For each linear or quadratic functions, are required to find the
domain, range, x-intercept, y-intercept, maxima, minima, end
behavior, discontinuities, asymptote; asymmetry. Also graph the
functions. Be sure to show all your work
1. f(x) = 3x+ 2
2. f(x) = 1/2X – 4

Consider the function
f(x)=
x3
x2 − 4
Express the domain of the function in interval notation:
Find the y-intercept: y=
.
Find all the x-intercepts (enter your answer as a
comma-separated list): x=
.
On which intervals is the function positive?
On which intervals is the function negative?
Does f have any symmetries?
f is even;f is
odd; f is periodic;None of the
above.
Find all the asymptotes of f (enter your answers as
equations):
Vertical asymptote (left):
;
Vertical...

Let
f(x)=(x^2)/(x-2) Find the following
a) Domain of f
b) Intercepts (approximate to the nearest thousandth)
c) Symmetry (Show testing for symmetry)
d) asymptotes
e) Intervals of increase/decrease (approximate the critical
numbers to the nearest thousandth. Be sure to show the values
tested)
f) Local maxima and local minima
g) Intervals of concavity and points of inflection (be sure to
show all testing)
h) summary for f(x)=(x^2)/(x-2)
Domain
X intercepts:
Y intercept:
symmetry:
asymptote:
increasing:
decreasing:
local max:
local min:...

Let f(x) = x3 + 3x2 − 9x − 27 . The first
and second derivatives of f are given below.
f(x) = x3 + 3x2− 9x − 27 = (x − 3)(x +
3)2
f '(x) = 3x2 + 6x − 9 = 3(x − 1)(x + 3)
f ''(x) = 6x + 6 = 6(x + 1)
a.) Find the x-intercepts on the graph of f.
b.)Find the critical points of f.
c.) Identify the possible inflection points...

Given f(x)= x3 -
6x2-15x+30
Determine f ’(x)
Define “critical point” of a function. Then determine the
critical points of f(x).
Use the sign of f ’(x) to determine the interval(s) on which
the function is increasing and the interval(s) on which it is
decreasing.
Use the results from (c) to determine the location and values
(x and y-values of the relative maxima and the relative minima of
f(x).
Determine f ’’(x)
On which intervals is the graph of f(x)...

f(x)= log2(-x+2)-1, find the domain, range, asymptote, x and y
intercept for f and evaluate at x=-4

Let f(x) = x3 + 3x2 - 24x - 10
a) Find the intervals on which f is increasing/decreasing, and
find all local maximum and local minimum values of f.
b) Find all intervals on which f is concave up/concave down, and
find all inflection points of f.

Given the function f(x) = x3 - 3x2 - 9x + 10
Find the intervals where it is increasing and
decreasing and find the co-ordinates of the relative maximums &
minimums.
Find the intervals where it is concave up and down and
co-ordinates of any inflection points
Graph the f(x)

Given the functions f(x,y) = x3 + y3- 3x - 3y
First find the coordinates of all the critical
points of f(x,y) and then apply the Second Order Partial Derivative
Test to locate all relative maxima, relative minima and saddle
points of f(x,y). Justify your answers and show your conclusions
using an appropriate table.
[Hint: The domain of f(x,y) is an open region
]

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