Exam 3: Functions and Graphs

After opening the parachute, the descent of a parachutist follows a linear model. At 3:31 P.M., the height of the parachutist is 2800 feet. At 3:32 P.M., the height is 1600 feet. Use a linear equation that gives the height of the parachutist in terms of the time to find the time when the parachutist will reach the ground.

An open box is to be made from a square piece of cardboard having dimensions 22 inches by 22 inches by cutting out squares of area $x ^ { 2 }$ from each corner as shown in the figure below. If the volume of the box is given by $V ( x ) = 484 x - 88 x ^ { 2 } + 4 x ^ { 3 },$ state the domain of V . $22 - 2 x$ $22 - 2 x$

Describe the increasing, decreasing, and constant behavior of the function. Find the point or points where the behavior of the function changes. $f ( x ) = 2 x$

Given $x ^ { 2 } + y ^ { 2 } = 4$ , use the algebraic tests to determine symmetry with respect to both axes and the origin.

Find the slope of the line that passes through the points $( 7 , - 2 )$ and $( 7 , - 3 ).$

Which set of ordered pairs represents a function from P to Q? P = {5, 10, 15, 20} Q = {-2, 0, 2}

Evaluate the function at each specified value of the independent variable. $f ( x ) =$ a) $f ( 2 )$ b) $f ( 2.5 )$ c) $f ( - 2.5 )$ d) $f ( - 4 )$

Find all real values of x such that f (x) = 0. $f ( x ) = 4 x ^ { 2 } - 25$

Evaluate the function at the specified value of the independent variable and simplify. g (s) = -6s + 3; g (-0.2)

Find the slope and y-intercept of the equation of the line. $y = 3 x - 4$

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (-8, 0), (4, -3) L2 : (0, 1), (-4, 2)

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

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (1, 9), (-4, 8) L2 : (8, -7), (7, -1)

Find the domain of the function. $f ( y ) = \frac { - 6 y } { y + 9 }$

The simple interest on an investment is directly proportional to the amount of the investment. By investing $8750 in a certain certificate of deposit, you obtained an interest payment of $210.00 after 1 year. Determine a mathematical model that gives the interest, I, for this CD after 1 year in terms of the amount invested, P.

Find an equation of a circle that satisfies the following condition. Write your answer in standard form. Center: $( 1,2 )$ ; passing through $( 5 , - 3 )$

Which graph represents the function? $g ( x ) = \llbracket 2 x \rrbracket$

Determine if lines $L _ { 1 }$ and $L _ { 2 }$ are parallel, perpendicular, or neither. $L _ { 1 } : 4 x - 4 y = - 4$ $L _ { 2 } : 8 x + 8 y = 9$

The inventor of a new game believes that the variable cost of producing the game is $3.75 per unit and the fixed costs are $5000. The inventor sells each game for $8.99. Let $x$ be the number of games sold. Write the average cost per unit $\bar { C } = C / x$ as a function of $x$ where $C$ is defined as the total cost of producing $x$ games.

Sketch the graph of the function. $f ( x ) = x ^ { 2 } - 9$