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Magazine Problem 7
Find all real numbers (if any) that are fixed points for the given functions. $$f(t)=t^{2}-t+1$$
Problem 8
You are asked to express one variable as a function of another. Be sure to state a domain for the function that reflects the constraints of the problem. The product of two numbers is \(16 .\) Express the sum of the squares of the two numbers as a function of a single variable.
Problem 8
Find the linear functions satisfying the given conditions. The \(x\) - and \(y\) -intercepts of the inverse function are 5 and \(-1,\) respectively.
Problem 8
(a) Find the domain, \(x\) - and \(y\) -intercepts, vertical asymptotes, and horizontal asymptotes for each rational function. (b) Use a graphing utility to graph the function. Check to see that the graph is consistent with your results in part (a). $$y=\left(x^{3}-27\right) /\left(x^{4}-2 x^{3}+9 x^{2}-18 x\right)$$
Problem 8
Graph the quadratic function. Specify the vertex, axis of symmetry, maximum or minimum value, and intercepts. $$y=2(x+2)^{2}+4$$
Problem 8
The perimeter of a rectangle is 12 m. Find the dimensions for which the diagonal is as short as possible.
Problem 8
Sketch the graph of each function and spec. ify all \(x\) - and \(y\) -intercepts. $$y=-(x+2)^{3}$$
Problem 8
Find all real numbers (if any) that are fixed points for the given functions. $$F(t)=t^{2}-t-1$$
Problem 9
Sketch the graph of each function and spec. ify all \(x\) - and \(y\) -intercepts. $$y=(x-4)^{3}-2$$
Problem 9
Let \(f(x)=3 x-4\) and \(g(x)=1-2 x .\) Determine whether the function \(f \circ g\) is linear.
