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Chapter 1: Problem 47
Write an equation for the function described by the given characteristics. The shape of \(f(x)=x^{2},\) but shifted three units to the right and seven units down
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Evaluate the function for the indicated values. \(k(x)=\left[\frac{1}{2} x+6\right]\) (a) \(k(5)\) (b) \(k(-6.1)\) (c) \(k(0.1)\) (d) \(k(15)\)
The height \(y\) (in feet) of a baseball thrown by a child is $$y=-\frac{1}{10} x^{2}+3 x+6$$ where \(x\) is the horizontal distance (in feet) from where the ball was thrown. Will the ball fly over the head of another child 30 feet away trying to catch the ball? (Assume that the child who is trying to catch the ball holds a baseball glove at a height of 5 feet.)
Find the difference quotient and simplify your Answer: $$f(x)=x^{2}-x+1, \quad \frac{f(2+h)-f(2)}{h}, \quad h \neq 0$$
Find a mathematical model that represents the statement. (Determine the constant of proportionality.) Use the fact that 14 gallons is approximately the same amount as 53 liters to find a mathematical model that relates liters \(y\) to gallons \(x\) Then use the model to find the numbers of liters in 5 gallons and 25 gallons.
(a) Write the linear function \(f\) such that it has the indicated function values and (b) Sketch the graph of the function. $$f(1)=4, \quad f(0)=6$$
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