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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
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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 1, y2 = af(x) is a vertical stretch by a factor of a away from the x-axis of
the graph y1 = f(x); whereas if 0 < a 1, y3 = f(bx) is a horizontal compression by a factor of 1/b toward the yaxis of y1 = f(x); whereas if 0 < b < 1, y3 = f(bx) is a horizontal stretch by a factor
of 1/b away from the y-axis of y1 = f(x).
147.
148.
149. f(x) = x
2
, g(x) = 15x
2
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