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Chapter 1: Problem 24
Evaluate (if possible) the function at each specified value of the independent variable and simplify. \(h(t)=t^{2}-2 t\) (a) \(h(2)\) (b) \(h(1.5)\) (c) \(h(x+2)\)
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Find the difference quotient and simplify your Answer: $$f(x)=x^{3}+3 x, \quad \frac{f(x+h)-f(x)}{h}, \quad h \neq 0$$
Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$h(x)=\sqrt{x+2}+3$$
During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate of 2 inches per hour for the next 6 hours, and at a rate of 0.5 inch per hour for the final hour. Write and graph a piecewise- defined function that gives the depth of the snow during the snowstorm. How many inches of snow accumulated from the storm?
Sketch the graph of the function. $$h(x)=\left\\{\begin{array}{ll}4-x^{2}, & x<-2 \\\3+x, & -2 \leq x<0 \\\x^{2}+1, & x \geq 0\end{array}\right.$$
Write the area \(A\) of a square as a function of its perimeter \(P\).
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