Exam 4: Additional Topics With Functions

The height h in feet of a frisbee thrown is given by $h ( x ) = x - 0.099 x ^ { 2 } + 3$ , where x is the time traveled in seconds. The frisbee is released at a height of 3 feet. At what time will the height of the frisbee be 3 feet again? (Round your answer to the nearest tenth of a second, if necessary.)

Determine if the function f defined by the set of ordered pairs has an inverse. If so, find the inverse. - $\{ ( 16,10 ) , ( 7,15 ) , ( - 1 , - 3 ) \}$

Determine if the function f defined by the set of ordered pairs has an inverse. If so, find the inverse. - {(3,-5),(5,-3),(9,2),(-9,-2)}

A function that models the population (in thousands) of children under the age of 18 in a certain town, t years after 2010 is C(t)=0.0013t²-0.163t+15.82 . A function that models the population (in thousands) of adults aged 18 or over of the same town, t years after 2010 is A(t)=0.0063t²-0.217t+25.08 . Find the equation of a function that models the estimated population of the town t years after 2010 .

The graphs of two functions f(x) and g(x) are given. -Solve $\mathrm { f } ( \mathrm { x } ) \leq \mathrm { g } ( \mathrm { x } )$ .

Solve the equation - $\sqrt { 2 x ^ { 2 } - 16 } - x = 0$

The linear equation y = 82.67x = 1181 provides an approximation of the va;ue (in dollars) of an account opend on january 1, 2010, in the amount of $1181 and earning 7% simple interest, where x = 0 represents january 1, 2010, x=1 represents january 1, 2011, x=2 represents january 1, 2012. and so on. Write an equation that yields the same y-values when the exact year number is entered.

Determine whether the function is even, odd, or neither. - $f ( x ) = \left| x ^ { 2 } + x \right|$

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - $( x - 10 ) ^ { 3 } > 66$

Use the given graph of f(x) $f ( x ) = a x ^ { 2 } + b x + c$ c to solve the specified inequality. - $\mathrm{f}(\mathrm{x})>0$

The differance between thr tuition at State University and Highbrow Collage is less than $900. The tuition at Highbrow is $5000. Express this as an absolute value inequality. Use "x" for the tuition of state University.

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - $f(x)=\sqrt{x+2}$

Find the specified domain and express it in interval notation. -If $f ( x ) = x ^ { 3 }$ and g(x)=x+2 , evaluate $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( - 2 )$

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f(x)=\sqrt{x}, g(x)=\sqrt{x-3}-2$

Find the specified domain and express it in interval notation. -For $f ( x ) = \sqrt { x - 5 }$ and $g ( x ) = x - 7$ , what is the domain of $f / g$ ?

A manufacturer of DVD players has monthly fixed costs of $5500 and variable costs of $50 per DVD player and it sells the DVD players for $150 per unit. Write the function that models the profit P from the production and Sale of x DVD players in a month.

The daily cost $C$ (in dollars) of removing pollution from the smokestack of an electric power plant is related to the percent of pollution $p$ removed according to the equation $C = \frac { 16,400 } { 100 - p }$ . Describe the transformations needed to obtain the graph of this function from the graph of $C = \frac { 1 } { \mathrm { p } }$ .

Find the inverse of the function. - $f ( x ) = 5 x + 3$

$\text { Solve } f ( x ) \leq g ( x )$

Find the inverse of the function. - $f ( x ) = x ^ { 3 } + 7$