Chapter 1: Q59E (page 7)
Find a formula for the function whose graph s the given curve.
The line segment joining the points \(\left( {{\bf{1}}, - {\bf{3}}} \right)\) and \(\left( {{\bf{5}},{\bf{7}}} \right)\).
The equation of line is \(y = \frac{5}{2}x - \frac{{11}}{2}\) for \(1 \le x \le 5\).
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Evaluate \(f\left( { - {\bf{3}}} \right)\), \(f\left( {\bf{0}} \right)\), and \(f\left( {\bf{2}} \right)\) for the piecewise defined function. Then sketch the graph of the function.
\(f\left( x \right) = \left\{ {\begin{aligned}{ - {\bf{1}}}&{{\bf{if}}\;\;x \le {\bf{1}}}\\{{\bf{7}} - {\bf{2}}x}&{{\bf{if}}\;\;x > {\bf{1}}}\end{aligned}} \right.\)
Evaluate the difference quotient for the given function. Simplify your answer.
38. \(f\left( x \right) = \sqrt {x + 2} \), \(\frac{{f\left( x \right) - f\left( 1 \right)}}{{x - 1}}\)
15-18 determine whether the curve is the graph of a function of \(x\). If it is, state the domain and range of the function.
18.
7-14 Determine whether the equation or table defines y as a function of x.
\({\bf{3}}x - {\bf{5}}y = {\bf{7}}\)
Find a formula for the function whose graph s the given curve.
The bottom half of the parabola \(x + {\left( {y - {\bf{1}}} \right)^{\bf{2}}} = {\bf{0}}\).
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