Graphs of Functions Discussion Assignment

Graphs of Functions Discussion Assignment
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Graphs of Functions Discussion Assignment
Basic Graphing Concepts
In questions 121 to 124, use a graphing utility to graph the function.
121. Graph y = x
2 – 4 and state its domain and range.
122. Graph and state its domain and range.
123. Graph y = x
3 and state its domain and range.
124. Graph and state its domain and range.
For questions 125 and 126, determine whether the graph shown is the graph of a
function. Explain your reasoning.
125.
126.
For questions 127 to 130, find the x- and y-intercepts.
127. f(x) = 6x – 1
128. f(x) = 6x
2 5x – 4
129. p(x) = (x 1)(x 3)(x – 2)(x – 4)
130. g(x) = x
2 4
Increasing and Decreasing Behavior and Extrema
For questions 131 to 133, use the graph of the function f to determine intervals
where f is increasing, decreasing, or constant. Refer to the following definitions,
as needed.
A function f is strictly increasing on an interval I if, for every pair of numbers x1
and x2
in I, f(x1) < f(x2) whenever x1 f(x2) whenever x1 < x2
; f is constant on I if
f(x1) = f(x2) for every pair of numbers x1 and x2
in I.
131.
132.
133.
Graphs of Functions Discussion Assignment
For questions 134 to 137, use the graph of the function f to determine any
relative or absolute extrema. Refer to the following definitions, as needed.
f(c) is an absolute minimum of f if f(c) ≤ f(x) for all x in Df
. Similarly, f(c) is an
absolute maximum of f if f(c) ≥ f(x) for all x in Df
. The minimum and maximum
values are the extrema. f(c) is a relative minimum of f if there exists an open
interval containing c in which f(c) is a minimum; similarly, f(c) is a relative
maximum of f if there exists an open interval containing c in which f(c) is a
maximum. If f(c) is a relative minimum or maximum, it is called a relative
extremum.
134.
135.
136.
137.
Function Transformations
For questions 138 to 142, write the equation for the graph of the function g that
results when the given transformation is applied to the function f. Do not
simplify the equation.
138. A vertical shift of 7 units up of the graph defined by f(x) = .
139. A horizontal shift of 7 units to the right of the graph defined by f(x) = .
140. A vertical shift of unit down of the graph defined by f(x) = |x|.
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