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06:21Composition of Functions
A balloon’s volume V is given by V = s² + 2s + 3 cm³, where s is the ambient temperature in °C. The ambient temperature s at time t minutes is given by s = 2t − 3 °C. Write the balloon’s volume V as a function of time t.
Graphing
In Exercises 69–76, graph each function not by plotting points, but by starting with the graph of one of the standard functions presented in Figures 1.14–1.17 and applying an appropriate transformation.
y = (−2x)²/³
Radians and Degrees
On a circle of radius 10 m, how long is an arc that subtends a central angle of (a) 4π/5 radians? (b) 110°?
Finding a Viewing Window
In Exercises 5–30, find an appropriate graphing software viewing window for the given function and use it to display that function’s graph. The window should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss important aspects of the function.
f(x) = (x² − 1)/(x² + 1)
Finding Formulas for Functions
A point P in the first quadrant lies on the graph of the function f(x) = √x. Express the coordinates of P as functions of the slope of the line joining P to the origin.
Piecewise-Defined Functions
In Exercises 35 and 36, find the (a) domain and (b) range.
𝔂 = { √ -x, -4 ≤ x ≤ 0
{ √ x, 0 < x ≤ 4
