Exam 3: Functions and Graphs

Solve the problem. -A ball is thrown vertically upward at an initial speed of $54 \mathrm{ft} / \mathrm{sec}$ . Its height (in feet) after $t$ seconds is given by $h(t)=t(54-16 t)$ What is the height of the ball after 2.7 seconds?

Solve the problem. -Find $f(5)$ for $f(x)=\left\{\begin{array}{l}5 x+1 \text { if } x<1 \\ 5 x \text { if } 5 \leq x \leq 9 \\ 5-9 x \text { if } x>9\end{array}\right.$

Solve the problem. -Suppose that the change in pressure of the oil in a reservoir can be approximated by: $P(x)=x^{3}-18 x^{2}+81 x$ Where $x$ is time in years from the date of the first reading. This function is valid for $0 \leq x<9$ . By sketching a graph of $\mathrm{P}(\mathrm{x})$ , estimate during what time period the change in pressure is decreasing.

Use the vertical line test to determine if the graph is a graph of a function. -

Graph the function. - $y=4 x^{2}$

Find the $x$ and $y$ intercepts. If no $x$ intercepts exist, state so. - $f(x)=2 x^{2}-8 x-24$

Graph the polynomial function. - $f(x)=x^{4}+2$

Solve the problem. -Find $f(0)$ for $f(x)=\left\{\begin{array}{cc}X-6 & \text { if } x<6 \\7-x & \text { if } x \geq 6\end{array}\right.$

Solve the problem. -Suppose that the change in pressure of the oil in a reservoir can be approximated by: $P(x)=x^{3}-24 x^{2}+144 x$ Where $x$ is time in years from the date of the first reading. This function is valid for $0 \leq x<12$ . By sketching a graph of $\mathrm{P}(\mathrm{x})$ , estimate when the change in pressure is maximum.

State the domain of the given function. - $f(x)=-5 x+3$

Graph the polynomial function. - $P(x)=\frac{1}{5} x^{4}$

Graph the linear function. - $f(x)=-4 x+1$

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3, 4, 5, 6 .

Use the graph to solve the problem. -In one city, the temperature in Fahrenheit on a typical summer day can be approximated by the following function: $f(x)= \begin{cases}53+3.8 t & \text { if } 0 \leq t \leq 7 \\ 79.6 & \text { if } 7<t \leq 10 \\ -5.4 t+133.6 & \text { if } 10<t \leq 15\end{cases}$ Here, $t$ represents the number of hours since 6 a.m. The graph of this function is shown below. At what time is the temperature the highest?

Solve the problem. -Assume that the sales of a computer retail store are approximated by a linear function. Sales were $\$ 820,000$ in 1982 and $\$ 2,640,000$ in 1987 . Let $x=0$ represent 1982 . Find the equation giving yearly sales. Estimate sales in 1990.

Use the graph to solve the problem. -In one city, the temperature in Fahrenheit on a typical summer day can be approximated by the following function: $f(x)= \begin{cases}53+3.8 t & \text { if } 0 \leq t \leq 7 \\ 79.6 & \text { if } 7<t \leq 10 \\ -5.4 t+133.6 & \text { if } 10<t \leq 15\end{cases}$ Here, $t$ represents the number of hours since 6 a.m. The graph of this function is shown below. Use the graph to estimate the temperature at 7 a.m.

Find the appropriate linear cost or revenue function. -A cable TV company charges $\$ 27$ for the basic service plus $\$ 6$ for each movie channel. Let $C(x)$ be the total cost in dollars of subscribing to cable TV, using $x$ movie channels. Find the linear cost function.

Find a quadratic function that models the data. -The table lists the total precipitation in six consecutive months in one U.S. city. Let $\mathrm{x}=0$ correspond to July and let $\mathrm{f}(\mathrm{x})$ be the total precipitation in month $\mathrm{x}$ . Using $(0,0.6)$ as the vertex and $(5,5.7)$ as the other point, determine a quadratic function $f(x)=a(x-h)^{2}+k$ that models the data.

Graph the piecewise linear function. - $f(x)= \begin{cases}x-1, & x>2 \\ -4, & x<2\end{cases}$

Write a cost function for the problem. Assume that the relationship is linear. -A moving firm charges a flat fee of $\$ 30$ plus $\$ 25$ per hour. Let $C(x)$ be the cost in dollars of using the moving firm for $x$ hours.