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Chapter 1: Problem 80
Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=x^{2}-5 x+8$$
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Explain how to find the difference quotient of a function \(f\) \(\frac{f(x+h)-f(x)}{h},\) if an equation for \(f\) is given.
Define a piecewise function on the intervals \((-\infty, 2],(2,5)\) and \([5, \infty)\) that does not "jump" at 2 or 5 such that one piece is a constant function, another piece is an increasing function, and the third piece is a decreasing function.
What is a piecewise function?
Determine whether each statement makes sense or does not make sense, and explain your reasoning. To avoid sign errors when finding \(h\) and \(k,\) I place parentheses around the numbers that follow the subtraction signs in a circle's equation.
Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+8 x+4 y+16=0$$
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