Exam 1: Graphs and Models

$\text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x ) + 4 \text {. }$

Determine whether the function is even, odd, or neither. $f ( x ) = x \sin 2 x$

$\text { Which of the following is the correct graph of } y = 3 x - x ^ { 2 } \text { ? }$

Table given below shows the Consumer Price Index (CPI) for selected years. The mathematical model for the data given below is $y = - 0.031 t ^ { 2 } + 5.887 t + 24.429$ , where $y$ represents the CPI and $t$ represents the year, with $t = 5$ corresponding to 1975 . Use the model to predict the CPI for the year 2010. Round your answer to the nearest integer. ear 975 980 985 990 995 000 005 PI 2.8 0 06.6 30.7 52.4 71.2 94.3

all intercepts: $y = ( x + 5 ) \sqrt { 4 - x ^ { 2 } }$

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { \frac { 7 } { 17 } }$

Let $g ( x ) = \frac { 1 } { \sqrt { x + 15 } }$ . Evaluate the expression $\frac { g ( x ) - g ( - 11 ) } { x + 11 }$ and then simplify the result. $g ( x ) = \frac { 1 } { \sqrt { x + 15 } } , \frac { g ( x ) - g ( - 11 ) } { x + 11 }$

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x )$ $=3 \sqrt[5]{8 x-9}$

$\text { Find the slope of the line passing through the points } \left( - \frac { 1 } { 8 } , \frac { 8 } { 3 } \right) \text { and } \left( - \frac { 3 } { 16 } , \frac { 1 } { 24 } \right) \text {. }$

$\text { A real estate office handles an apartment complex with } 50 \text { units. When the rent is }$ $\$ 800$ per month, all 50 units are occupied. However, when the rent is $\$ 845$ , the average number of occupied units drops to 47 . Assume that the relationship between the monthly rent $p$ and the demand $x$ is linear. Write a linear equation giving the demand $x$ in terms of the rent $p$ .

The resistance $y$ in ohms of 1000 feet of solid metal wire at $77$ $F^{\circ}$ can be approximated by the model $y = \frac { 12,750 } { x ^ { 2 } } - 0.37,5 \leq x \leq 100$ , where $x$ is the diameter of the wire in mils $( 0.001$ in $)$ . If the diameter of the wire is doubled, the resistance is changed by approximately what factor? In determining your answer, you can ignore the constant $- 0.37$ .

$\text { Find the domain and range of the function } h ( x ) = \frac { 11 } { x + 6 } \text {. }$

$\text { Evaluate (if possible) the function } g ( x ) = x ^ { 2 } ( x + 2 ) \text { at } x = t - 6 \text {. Simplify the result. }$

Find the coordinates of a second point on the graph of a function f if the given point $\left( - \frac { 9 } { 8 } , 5 \right)$ is on the graph and the function is odd.

$\text { Find the domain and range of the function } g ( t ) = \sqrt { t - 10 } \text {. }$

You need 50 pounds of two commodities costing $1.60 and $1.95 per pound. Determine the number of pounds of the less expensive commodity purchased if the total cost $y = 1.60 x + 1.95 ( 50 - x )$ is $\$ 94$ .

$\text { What is the domain of the function } f ( x ) = 6 \ln ( 4 x ) ?$

Hooke's Law states that the force F required to compress or stretch a spring (within its elastic limits) is proportional to the distance $d$ that the spring is compressed or stretched from its original length. That is, $F = k d$ where $k$ is a measure of the stiffness of the spring and is called the spring constant. The table shows the elongation $d$ in centimeters of a spring when a force of $F$ newtons is applied. Use a graphing utility to plot the data and graph the linear model. F 20 40 60 80 100 d 1.3 2.6 3.9 5.2 6.5

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = 6 x ^ { 2 } , x \geq 0 \text {. }$

$\text { Solve the following equation for } x \text {. }$ $- 5 + 7 e ^ { 3 x } = 10$