Exam 13: Functions

The cost for burning a 75-watt bulb is given by the function c ( h ) = 0.0045 h , where h represents the number of hours that the bulb burns. How much does it cost to burn a 75-watt bulb for 4 hours per night for a 30-day month? Express your answer to the nearest cent. $ __________

Suppose that the profit function for selling n items is given by $P ( x ) = - n ^ { 2 } + 750 n - 49,300$ where n represents the number of items produced. Find $P ( 150 ) , P ( 175 ) , P ( 250 ) , P ( 300 )$ .

Specify the domain for the function. Please enter your answer in interval notation. $f ( x ) = \frac { 6 } { x - 6 }$

The set of all second components of the ordered pairs of a relation is called the range.

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \sqrt { x + 9 } \text { and } g ( x ) = 5 x + 9$

If g ( x ) = 8 x + 4 and f ( x ) = 5 x 2 $-$ 9, find $( f \circ g ) ( 4 ) \text { and } ( g \circ f ) ( 4 )$ . Match each expression with the corresponding answer. - $572$

Determine $( g \circ f ) ( x )$ for the pair of functions f ( x ) = 2 x + 9 and g ( x ) = x 2 + 9.

The function $f ( x ) = 2 x + 5$ is a linear function.

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x ) = $-$ 3 x + 6.

Specify the domain for the function. Please enter your answer in interval notation. $f ( x ) = \frac { - 7 } { x ^ { 2 } + 3 x }$

If V varies jointly as B and h , and V = 30 when B = 10 and h = 6, find V when B = 5 and h = 16.

Given $g ( x ) = x ^ { 2 } - 1$ , the notation $g ( 4 )$ means to find the value of g when x is 4.

The volume ( Z ) of a gas varies directly as the absolute temperature ( Q ) and inversely as the pressure ( D ). Translate the statement of variation into an equation and use k as the constant of variation.

Direct and inverse variation may not occur in the same problem.

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions f ( x ) = 2 x + 3 and g ( x ) = x 2 + 9.

Find the constant of variation for the stated condition: y varies directly as x , and y = 225 when x = 100.

Find two numbers whose sum is 60 and whose product is a maximum. Please enter your answer as two numbers separated by a comma, without the units.

If f ( x ) = 2 x + 6, find f (0), f ( $-$ 5), f (4), f ( $-$ 9).

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $46,000 and it depreciates $850 each year for t years. Find the value of the machinery after 4 years. $ __________

Specify the domain for the function. Please enter your answer in interval notation. $f ( x ) = \sqrt { x ^ { 2 } - 25 }$