Exam 4: Additional Topics With Functions

Determine whether the function is one-to-one. -The function that pairs the temperature at 3:00 pm in your city in degrees Fahrenheit with the temperature in degrees Celsius.

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. -y= x+ $\frac { 1 } { x ^ { 4 } }$

Determine whether or not the function is one-to-one. - $f ( x ) = \left| 9 - x ^ { 2 } \right|$

The number of people present at a stadium holding a big rock concert can be estimated with the following function: $y = 13252 x ^ { 0.74 } + 0.54 x + 102$ where y is the number of people present and x is the amount of time since 3:00 p.m. on the day of the concert. Rewrite the model with x equal to the amount of time since 1.00 p.m.

Find the specified domain and express it in interval notation. -If f(x)=x-3 and g(x)=x+3 , evaluate $( f \cdot g )$ (-2).

Decide whether or not the functions are inverses of each other. - $f ( x ) = 9 x - 8 , g ( x ) = \frac { x + 9 } { 8 }$

The supply function for a product is $p ( x ) = \frac { 1 } { 3 } x ^ { 2 } + 50$ where x is the number of thousands of units a manufacturer will supply if the price is p(x) dollars. Find the inverse of this function.

Find the specified domain and express it in interval notation. -For $f ( x ) = \sqrt { x - 4 }$ and $g ( x ) = \frac { 1 } { x - 6 }$ , what is the domain of $g / f$ ?

Determine if the complete graph represents a function that is even, odd, or neither. -

Find the inverse of the function. - $f ( x ) = 5 x ^ { 3 } + 7$

Determine whether or not the function is one-to-one. -

Let C(x) = 500+70x be the cost to manufacture x times. Find the avarage cost per item to produce 30 items.

A size 12 dress in Country C is size -22 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x)= x -34 . Find a formula for the inverse of this function.

Find the requested composition of functions. -Given $f ( x ) = | 12 - x | \text { and } g ( x ) = 3 x + 8 \text {, find } ( g \text { of } ) ( x )$

The graph of the function y $y = f ( x ) \text { is given. On the same axes, sketch the graph of } f ^ { - 1 } ( x )$ . Use a dashed line for the inverse function. -

For the functions f and g, find the requested value. -Evaluate (f $\circ g ) ( 2 )$ .

Determine whether or not the function is one-to-one. -

Determine if the function f defined by the set of ordered pairs has an inverse. If so, find the inverse. - $\{ ( - 2,4 ) , ( 2 , - 4 ) , ( 8 , - 2 ) , ( - 8,2 ) \}$

At Allied Electronics, production has begun on the X-15 Computer Chip. The total revenue function is given by $R ( x ) = 59 x - 0.3 x ^ { 2 }$ and the total profit function is given by $P ( x ) = - 0.3 x ^ { 2 } + 57 x - 8$ where x represents the number of boxes of computer chips produced. The total cost function, C(x) , is such that C(x)=R(x)-P(x) . Find C(x) .

Determine whether the function is even, odd, or neither. - $y = \sqrt { x ^ { 2 } + 5 }$