91Ó°ÊÓ

Multiple Choice An odd function is symmetric with respect to (a) the \(x\) -axis (b) the \(y\) -axis (c) the origin (d) the line \(y=x\)

Multiple Choice A function that is continuous on the interval ________________ is guaranteed to have both an absolute maximum and an absolute minimum. (a) \((a, b)\) (b) \((a, b]\) (c) \([a, b)\) (d) \([a, b]\)

True or False If no domain is specified for a function \(f,\) then the domain of \(f\) is the set of real numbers.

Two cars are approaching an intersection. One is 2 miles south of the intersection and is moving at a constant speed of 30 miles per hour. At the same time, the other car is 3 miles east of the intersection and is moving at a constant speed of 40 miles per hour. (a) Build a model that expresses the distance \(d\) between the cars as a function of time \(t\). [Hint: At \(t=0,\) the cars are 2 miles south and 3 miles east of the intersection, respectively.] (b) Use a graphing utility to graph \(d=d(t) .\) For what value of \(t\) is \(d\) smallest?

Find the domain and range of each relation. Then determine whether the relation represents a function. \\{(-2,5),(-1,3),(3,7),(4,12)\\}

An open box with a square base is required to have a volume of 10 cubic feet. (a) Express the amount \(A\) of material used to make such a box as a function of the length \(x\) of a side of the square base. (b) How much material is required for such a box with a base 1 foot by 1 foot? (c) How much material is required for such a box with a base 2 feet by 2 feet? (d) Use a graphing utility to graph \(A=A(x) .\) For what value of \(x\) is \(A\) smallest? (e) What is the least amount of material needed?

Write the function whose graph is the graph of \(y=x^{3},\) but is: Vertically stretched by a factor of 5

Answer the questions about each function. $$f(x)=\frac{12 x^{4}}{x^{2}+1}$$ (a) Is the point (-1,6) on the graph of \(f ?\) (b) If \(x=3,\) what is \(f(x) ?\) What point is on the graph of \(f ?\) (c) If \(f(x)=1,\) what is \(x ?\) What point(s) are on the graph of \(f ?\) (d) What is the domain of \(f ?\) (e) List the \(x\) -intercepts, if any, of the graph of \(f\). (f) List the \(y\) -intercept, if there is one, of the graph of \(f\).

(a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. $$f(x)=\left\\{\begin{array}{ll}2 x & \text { if } x \neq 0 \\\1 & \text { if } x=0\end{array}\right.$$

Find the function that is finally graphed after each of the following transformations is applied to the graph of \(y=\sqrt{x}\) in the order stated. (1) Vertical stretch by a factor of 3 (2) Shift up 4 units (3) Shift left 5 units