- Given f x = 2 x
2 4 x, using the domain of 1 x 3 to graph the following functions:
f x , 2 f x , 4 f x , f x , 2 f x , and 4 f x on the same x-y coordinate system,
Explain the effect as you multiply the function by a constant. - Given the functions: h x = x
x
2
x 2
a) Use the Maple command to separate the denominator.
b) Find the zeros of the denominator.
c) Find the vertical asymptotes.
d) Confirm your answer to part (c) by graphing the function. - Given the following functions:
f x = sin x , g x = cos x , and h x = tan x
a) Plot the graphs of f x , g x , and h x on the same axes.
b) Plot the function a x = 2 sin 3 x
x
2 . - Given the function f x = x
4 1
x
2
x
,
use Maple to evaluate the limit as x approaches 1 algebraically (use a spreadsheet), numerically (use the
limit command), and graphically (use the plot command). - Given g x = x 1 x 4
x 4 x 4 , plot the function , is g(x) continuous at x=4? - Using Maple, evaluate the following limit. Verify your results graphically and algebraically, if possible.
a) limx 3
2 x 2
x 3 b) limx 0
1
x 1
x
1 - Evaluate the following discontinuities:
a) Find the discontinuities, if any, for the following functions
b) For each discontinuity, indicate whether it is removable or non-removable.
c) Use Maple to verify your results graphically, then confirm your results algebraically by evaluating the
appropriate limit.
a) f x = x 1
x
3
x 2
b) g x =
x
2 2 , x 2
5 , 2 x 0
8 x 5 , x 0 - Given the function g x =
8 2 x x 4
x 4 x 4
a) Find the limit of g(x) as x approaches the value "4" indicated below.
To do this, compute a table of values of "x" and the corresponding f(x) where "x" takes on the values
getting closer and closer to "4" from both sides of "4".
b) For the function g(x) given above,determine if g(x) is continuous at c=4. - Graph the function h x = 3 x
4 x
2
1
a) Locate any vertical and horizontal asymptotes.
b) Find the limit as x approaches positive and negative infinity.
c) Determine if h(x) is continuous at x=0.
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