91Ó°ÊÓ

Determine algebraically whether the function is even, odd, or neither even nor odd. Then check your work graphically, where possible, using a graphing calculator. $$f(x)=\frac{1}{x^{2}}$$

Determine algebraically whether the function is even, odd, or neither even nor odd. Then check your work graphically, where possible, using a graphing calculator. $$f(x)=8$$

For each piecewise function, find the specified function values. $$\begin{aligned} &g(x)=\left\\{\begin{array}{l} x+4, \text { for } x \leq 1 \\ 8-x, \text { for } x>1 \end{array}\right.\\\ &g(-4), g(0), g(1), \text { and } g(3) \end{aligned}$$

In economics, functions that involve revenue, cost, and profit are used. For example, suppose that \(R(x)\) and \(C(x)\) denote the total revenue and the total cost, respectively, of producing a new grocery cart for Ogata Wholesalers. Then the difference $$ P(x)=R(x)-C(x) $$ represents the total profit for producing \(x\) carts. Given \(R(x)=60 x-0.4 x^{2}\) and \(C(x)=3 x+13\) find each of the following. A. \(P(x)\) B. \(R(100), C(100),\) and \(P(100)\) C. Using a graphing calculator, graph the three functions in the viewing window \([0,160,0,3000]\)

Find \(f(x)\) and \(g(x)\) such that \(h(x)=(f \circ g)(x)\) Answers may vary. $$h(x)=\sqrt{\frac{x-5}{x+2}}$$

A stone is thrown into a pond, creating a circular ripple that spreads over the pond in such a way that the radius is increasing at a rate of \(3 \mathrm{ft} / \mathrm{sec}\). (IMAGE CANNOT COPY) a) Find a function \(r(t)\) for the radius in terms of \(t\) b) Find a function \(A(r)\) for the area of the ripple in terms of the radius \(r\) c) Find \((A \circ r)(t) .\) Explain the meaning of this function.

Write an equation for a function that has a graph with the given characteristics. The shape of \(y=x^{3},\) but reflected across the \(x\) -axis and shifted right 5 units

Write an equation for a function that has a graph with the given characteristics. The shape of \(y=1 / x,\) but shrunk horizontally by a factor of 2 and shifted down 3 units

Determine whether the graph is symmetric with respect to the \(x\) -axis, the \(y\) -axis, and the origin. $$\left(x^{2}+y^{2}\right)^{2}=2 x y$$ (GRAPH CAN'T COPY)

Consider the following linear equations. Without graphing them, answer the questions below. a) \(y=x\) \(\quad\) b) \(y=-5 x+4\) \(\quad\) c) \(y=\frac{2}{3} x+1\) \(\quad\) d) \(y=-0.1 x+6\) \(\quad\) e) \(y=3 x-5\) \(\quad\) f) \(y=-x-1\) \(\quad\) g) \(2 x-3 y=6\) \(\quad\) h) \(6 x+3 y=9\) Which has the steepest slope?