Chapter 1: Q18 E (page 1)
Find a polar equation for the curve represented by the given Cartesian equation.
\({{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}{\rm{ = 2}}\)
The polar equation of the curve \({{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}{\rm{ = 2}}\) is \({\rm{r = }}\sqrt {\rm{2}} \).
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Express the function in the form \({\bf{f}} \circ {\bf{g}}\)
\({\bf{F}}\left( {\bf{x}} \right){\bf{ = co}}{{\bf{s}}^{\bf{2}}}{\bf{x}}\)
The graph of\({\bf{f}}\)is given. Draw the graphs of the following functions.
(a)\({\bf{y = f}}\left( {\bf{x}} \right){\bf{ - 2}}\)
(b)\({\bf{y = f}}\left( {{\bf{x - 2}}} \right)\)\(\)
(c)\({\bf{y = - 2f}}\left( {\bf{x}} \right)\)
(d)\({\bf{y = f}}\left( {\frac{{\bf{1}}}{{\bf{3}}}{\bf{x}}} \right){\bf{ + 1}}\)
Find the functions (a)\({\bf{f}} \circ {\bf{g}}\), (b)\({\bf{g}} \circ {\bf{f}}\), (c)\({\bf{f}} \circ {\bf{f}}\), (d) \({\bf{g}} \circ {\bf{g}}\) and their domains.
\({\bf{f}}\left( {\bf{x}} \right){\bf{ = 1 - 3x}}\) \({\bf{g}}\left( {\bf{x}} \right){\bf{ = cosx}}\)
The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function\({\bf{f = }}\frac{{\bf{9}}}{{\bf{5}}}{\bf{c + 32}}{\bf{.}}\)
(a) Sketch a graph of this function
(b)What is the slope of the graph and what does it represent? What is the
F-intercept and what does it represent?
A rectangle has area\({\bf{16}}\;{{\bf{m}}^{\bf{2}}}\). Express the perimeter of the rectangle as a function of the length of one of its sides.
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