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Graphical Representations of Different Functions

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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

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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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Graphical representation of functions

1. Give an example of an exponential function. Convert this exponential function to a logarithmic function. Plot the graph of both the functions and post to the discussion forum. Discuss these functions and their graphs with your classmates.

2. Given the values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, x, and y, form each of the following:

? A linear equation in one variable
? A linear equation in two variables
? A quadratic equation
? A polynomial of three terms
? An exponential function
? A logarithmic function

Compare all the functions written by you and discuss their differences.

3. Plot the graph of the above equations formed by you (in question 2) and post your response to the discussion forum. Label your graphs correctly.

4. How do you think the knowledge of graphical representation of these functions will help you in your career or in the future?

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