Exam 3: Functions and Graphs

Solve the problem. -On a business trip, Jon must drive from his office to a clients's office, a distance of 204 miles. He sets off a $8 \mathrm{a} . \mathrm{m}$ . Suppose that he drives at a constant speed of $67 \mathrm{mph}$ . Find the rule of the function $f(t)$ that gives his distance from the client's office at time $t$ hours (with $t=0$ corresponding to 8 a.m.)

Solve the problem. -Suppose that the number of frequent flier miles (in billions) earned by customers of various airlines, but not yet redeemed in year $\mathrm{x}$ , could be approximated by the polynomial function: $f(x)=0.0017 x^{4}-0.68 x^{3}+11.33 x^{2}-20.15 x \quad(3 \leq x \leq 14)$ Where $x=0$ corresponds 1980. How many unredeemed miles were there in 1991?

Graph the parabola. - $y=2(x-1)^{2}-2$

State whether the parabola opens upward or downward. - $f(x)=-4 x^{2}$

Find the $x$ and $y$ intercepts. If no $x$ intercepts exist, state so. - $f(x)=-x^{2}-3 x-4$

State whether the parabola opens upward or downward. - $f(x)=4(x-8)^{2}-6$

For the given function, find $\frac{f(x+h)-f(x)}{h}$ . - $9 x-3$

Graph the polynomial function. - $f(x)=x^{3}+4 x-1$

Solve the problem. -Suppose the cost of producing $x$ computers is $c(x)=2000+90 x-0.1 x^{2}$ . Find the cost of producing 80 computers.

Solve the problem. -A book publisher found that the cost to produce 1000 calculus textbooks is $\$ 27,200$ , while the cost to produce 2000 calculus textbooks is $\$ 51,300$ . Assume that the cost $C(x)$ is a linear function of $x$ , the number of textbooks produced. What is the marginal cost of a calculus textbook?

State the domain of the given function. - $f(x)=\frac{4}{2 x-9}$

Solve the problem. -Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $\$ 7500$ in 1982 and $\$ 62,000$ in 1987 . Let $x=0$ represent 1982 . Find the equation giving yearly sales $S(x)$ .

Evaluate the function. -Given that $f(x)=x^{4}-1.7 x^{2}-8.4 x$ , find $f(1.5)$ .

Find the rule of a quadratic function whose graph has the given vertex and passes through the given point. -vertex $(-4,2)$ ; point $(4,66)$

Write a cost function for the problem. Assume that the relationship is linear. -Fixed cost, $\$ 400 ; 10$ items cost $\$ 2350$ to produce

Solve the problem. -Suppose the supply and demand for a certain videotape are given by: $\text { supply: } \mathrm{p}=\frac{1}{6} \mathrm{q}^{2} ; \quad \text { demand: } \mathrm{p}=-\frac{1}{6} \mathrm{q}^{2}+33$ Where $\mathrm{p}$ is price and $q$ is quantity. How many videotapes are supplied at a price of $\$ 18$ ?

Match the function to the correct graph. - $y=x^{4}+x^{3}-5 x^{2}-4 x+4$

Graph the piecewise linear function. - $f(x)= \begin{cases}x-4, & x>0 \\ 5, & x \leq 0\end{cases}$

Graph the parabola. - $f(x)=(x+1)^{2}+5$

Graph the function. - $f(x)=\sqrt{x+5}$