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Graphical Representations of Different Functions

1. Use the graph of f(x)= x^ to match the function to its corresponding graph. In words describe the transformation that occurs (ex: The graph of f(x) is shifted 6 units to the left).
F(x) = x^
Give the following functions and Description of transformation and plot the graph of each.
a) G(x) = (x-2)^
b) H(x)= x^ -2
c) i(x) = (x+3)^
d) j(x)=(x+1)^+ 3

2. Find the domain of the function and express the answer in interval notation. Explain in words or show the calculations.
a) F(x) = 4x^ - 7x+3
b) G(x) = 10 / x+7
c) F(x) = sqrt( 4x-16)

3. Find the specified asymptotes of the following functions. Recall that asymptotes are lines therefore the answer must be given as an equation of a line.
a) Find the vertical asymptote of the function f(x) = 4/ x + 5
b) Find the horizontal asymptote of the function g(x) = 5x^-4/ x+1
c) Find the vertical and horizontal asymptotes of the function f(x) = 3x - 1/ x+4
d) Find the vertical and horizontal asymptotes of the function g (x) = x+7/x^ - 4

Solution Preview

Please see the attachment for the graphs.

1. Use the graph of f(x)= x^2 to match the function to its corresponding graph. In words describe the transformation that occurs (ex: The graph of f(x) is shifted 6 units to the left).
F(x) = x^2
Give the following functions and Description of transformation and plot the graph of each.
a) G(x) = (x-2)^2: the graph of f(x) is shifted 2 units to the right.

b) H(x)= x^2 -2: the graph of f(x) is shifted 2 units down

c) i(x) = (x+3)^2: the graph of f(x) is shifted 3 units to the left

d) j(x)=(x+1)^2+ 3 : the graph of f(x) is shifted 1 unit to the left, 3 units up.

2. Find the domain of the function and express the answer in interval notation. Explain in words or show the calculations.
a) F(x) = 4x^2 - 7x+3 ...

Solution Summary

The graphical representations of different functions are examined. The functions and descriptions of transformation and plot the graph is determined.

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