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Chapter 1: Problem 19
Determine whether the equation represents \(y\) as a function of \(x .\) $$y=-75$$
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Sketch the graph of the function. $$h(x)=\left\\{\begin{array}{ll}4-x^{2}, & x<-2 \\\3+x, & -2 \leq x<0 \\\x^{2}+1, & x \geq 0\end{array}\right.$$
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 statements use the word function in ways that are mathematically correct. Explain your reasoning. (a) The amount in your savings account is a function of your salary. (b) The speed at which a free-falling baseball strikes the ground is a function of the height from which it was dropped.
Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$k(x)=1 /(x-3)$$
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.)
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