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Chapter 1: Problem 69
Determine whether the lines \(L_{1}\) and \(L_{2}\) passing through the pairs of points are parallel, perpendicular, or neither. $$\begin{aligned} &L_{1}:(0,-1),(5,9)\\\ &L_{2}:(0,3),(4,1) \end{aligned}$$
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If \(f\) is an even function, determine whether \(g\) is even, odd, or neither. Explain. (a) \(g(x)=-f(x)\) (b) \(g(x)=f(-x)\) (c) \(g(x)=f(x)-2\) (d) \(g(x)=f(x-2)\)
Determine whether the statement is true or false. Justify your answer. A piecewise-defined function will always have at least one \(x\) -intercept or at least one \(y\) -intercept.
The inventor of a new game believes that the variable cost for producing the game is 0.95 dollars per unit and the fixed costs are 6000 dollars. The inventor sells each game for 1.69 dollars. Let \(x\) be the number of games sold. (a) The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost \(C\) as a function of the number of games sold. (b) Write the average cost per unit \(\bar{C}=C / x\) as a function of \(x .\)
Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=\frac{5}{6}-\frac{2}{3} x$$
Find a mathematical model that represents the statement. (Determine the constant of proportionality.) Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring.
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