Chapter 1: Q2E (page 7)
If \(f\left( x \right) = \frac{{{x^2} - x}}{{x - 1}}\) and \(g\left( x \right) = x\), is it true that \(f = g\)?
Yes, \(f = g\).
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Find the domain of the function.
40. \(f\left( x \right) = \frac{{{x^2} + 1}}{{{x^2} + 4x - 21}}\)
Three runner compete in a 100-meter race. The graph depicts the distance run as a function of time for each runner. Describe in words what the graph tells you about this race. Who won the race? Did each runner finish the race?
Determine whether f is even, odd, or neither. You may wish to use a graphing calculator or computer to check your answer visually.
86. \(f\left( x \right) = {\bf{1}} + {\bf{3}}{x^{\bf{3}}} - {x^{\bf{5}}}\)
If \(g\left( x \right) = \frac{x}{{\sqrt {x + 1} }}\), find \(g\left( 0 \right)\), \(g\left( 3 \right)\), \(5g\left( a \right)\), \(\frac{1}{2}g\left( {4a} \right)\), \(g\left( {{a^2}} \right)\), \({\left( {g\left( a \right)} \right)^2}\), \(g\left( {a + h} \right)\), \(g\left( {x - a} \right)\).
An airplane takes off from an airport and lands an hour later at another airport, 400 miles away. If t represents the time in minutes since the plane has left the terminal building, let \(x\left( t \right)\) be the horizontal distance traveled and \(y\left( t \right)\) be the altitude of the plane.
(a) Sketch a possible graph of \(x\left( t \right)\).
(b) Sketch a possible graph of \(y\left( t \right)\).
(c) Sketch a possible graph of ground speed.
(d) Sketch a possible graph of vertical velocity.
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