Exam 9: Functions

Find the inverse of the given function and express it in the form $y = f ^ { - 1 } ( x )$ . Verify the result by showing that $\left( f \circ f ^ { - 1 } \right) ( x ) = \left( f ^ { - 1 } \circ f \right) ( x ) = I ( x )$ . $x + 4 = 9 y$

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x )= -6 x + 2.

Determine whether the function is one-to-one. $f ( x ) = x ^ { 4 }$

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 9 x$ and $g ( x ) = 5 x - 5$ .

Find the inverse of the function and express it using $f ^ { - 1 } ( x )$ notation. $f ( x ) = 4 x ^ { 3 } - 2$

The time required for a car to travel a certain distance varies inversely as the rate at which it travels. If it takes 10 hours at 60 miles per hour to travel the distance, how long will it take at 100 miles per hour?

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

Identify the graph of the function. f ( x )= x ² + 6 x + 5

Determine both the domain and the range of the function. $y = f ( x ) = - 2 | x |$

If you have the following function f ( x )= 9 x + 7, compute f (1), f (-3), f (4), f (-6).

Use the vertical line test to determinate if curve is a function.

Graph the function $y = \sqrt { - x }$ .

The distance that a freely falling body falls varies directly as the square of the time it falls. If a body falls 640 feet in 8 seconds, how far will it fall in 13 seconds?

For the function, first sketch the graph of its associated function, $g ( x ) = x ^ { 3 }$ . Then draw the graph using a reflection. $f ( x ) = - x ^ { 3 }$

Graph the function $y = \frac { 1 } { x }$ .

Use the vertical line test to determinate if curve is a function.

Tell whether the equation determines y to be a function of x . y = 3.2 x + 8

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 2 hours per night for a 31-day month? Express your answer to the nearest cent.

Identify the graph of the function. f ( x )= x ² - 2 x - 1

Graph the function. $f ( x ) = - 5 \sqrt { x }$