Exam 11: Additional Properties of Functions

Indicate whether the function is one-to-one. -An oil well off the Gulf Coast is leaking, with the leak spreading oil over the surface of the gulf as a circle. At any time $t$ , in minutes, after the beginning of the leak, the radius of the oil slick on the surface is $r ( t ) = 4 t$ ft. Find the area A of the oil slick as a function of time.

Perform the requested operation on the given function. - $f ( x ) = 4 \sqrt { x - 6 } , g ( x ) = 2 \sqrt { x - 6 }$ Find $( f + g ) ( x )$

Perform the requested operation on the given function. - $f ( x ) = x ^ { 2 } - \frac { 4 } { 5 } x - 4 , g ( x ) = x ^ { 3 } + \frac { 3 } { 5 } x ^ { 2 } + x$ Find $( f + g ) ( x )$

Evaluate the function. -If $h ( x ) = \sqrt { x - 7 }$ , find $h \left( a ^ { 2 } + 17 \right)$

Indicate whether the function is one-to-one. -The surface area of a balloon is given by $S ( r ) = 4 \pi r ^ { 2 }$ , where $r$ is the radius of the balloon. If the radius is increasing with time $t$ , as the balloon is being blown up, according to the formula $r ( t ) = \frac { 4 } { 5 } t ^ { 3 } , t \geq 0$ , find the surface area $S$ as a function of the time $t$ .

Indicate whether the function is one-to-one. - $C = \{ ( 6 , - 9 ) , ( 2 , - 8 ) , ( 0 , - 7 ) , ( - 2 , - 6 ) \}$

Indicate whether the graph represents a one-to-one function -

Evaluate the function. -If $f ( x ) = \sqrt { x + 6 }$ , find $f ( 4 a + 2 )$

Fill in the blank. -To obtain the graph of f(x - k), shift the of f(x)k units.

Evaluate the function. -If $f ( x ) = 6 x - 11$ , find $f ( 0 )$

Indicate whether the function is one-to-one. -Suppose the dollar cost to produce $n$ items in a factory is $c ( n ) = 4 n + 3$ . Furthermore, the number of items $n$ produced in $x$ hours is $n ( x ) = 6 x$ . Find $c [ n ( x ) ]$ , which is the composite function that defines the dollar cost in terms of the number of hours of production $x$ .

Indicate whether the function is one-to-one. - $A = \{ ( - 5,16 ) , ( 16,16 ) , ( 2 , - 16 ) \}$

Find the composition. -If $f ( x ) = \frac { 3 } { x + 5 }$ and $g ( x ) = \frac { 1 } { 7 x }$ , find $f [ g ( x ) ]$

Solve -A rope 24 feet long is cut into two unequal pieces. Each piece is used to form a square. Let x represent the length of the shorter piece of rope. Write a function $\mathrm { A } ( \mathrm { x } )$ that expresses the total area enclosed by the two squares.

Evaluate the function. -If $r ( x ) = \frac { 3 } { x - 4 }$ , find $r ( a + 5 )$

Find the composition. -If $f ( x ) = 7 x ^ { 2 } + 4 x$ and $g ( x ) = 2 x$ , find $( f \circ g ) ( x )$

Evaluate the function. -If $r ( x ) = \frac { 6 } { x - 4 }$ , find $r ( - 3 )$