Exam 4: Additional Topics With Functions

For the functions f and g, find the requested value. -Evaluate $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 2 )$ .

Solve the equation - $( x + 5 ) ^ { 2 / 5 } = 16$

For the pair of functions, perform the indicated operation. - $f ( x ) = 2 x - 2 , g ( x ) = 5 x - 8 \quad$ Find $( f - g ) ( x )$

Use the quadratic formula or graphing methods to - $4 x ^ { 2 } > 4 x + 4$

Write the equation of the graph after the indicated transformation(s). -The graph of $y = x ^ { 2 }$ is shifted 2 units to the left. This graph is then vertically stretched by a factor of 6 and reflected across the $x$ -axis. Finally, the graph is shifted 8 units downward.

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - $( x - 4 ) ^ { 3 } < 108$

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 1 } { x + 3 }$

The price per unit of a product is $\$ \mathrm { p }$ and the number of units of the product is denoted by $\mathrm { q }$ . The demand function for this commodity is given by $\mathrm { p } = \frac { 20,000 } { \mathrm { q } } - 50$ . Describe the transformations needed to obtain the graph of this function from the graph of $p = \frac { 1 } { q }$ .

The volume of water added to a circular drum of radius r is given by $\mathrm { V } _ { \mathrm { w } } = 5 \mathrm { t } , \text { where } \mathrm { V } _ { \mathrm { w } }$ is volume in cu ft and t is time in sec. Find the depth of water in a drum of radius 3 ft after adding water for 4 sec. (Round result to one Decimal place.)

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

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f(x)=x^{3}, g(x)=-x^{3}-4$

Provide an appropriate response. -If f(x) represents the number of female millionaires in the United States and g(x) represents the number of male millionaires in the United States, with x equal to the number of years from 2000, then what function represents The total number of millionaires in the U.S. x years from 2000?

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f(x)=x^{3}, \quad g(x)=(x+4)^{3}$

Solve the equation - $\sqrt { x ^ { 2 } + 4 x } = \sqrt { - 6 x - 24 }$

Find the requested composition of functions. -Given $f ( x ) = \sqrt { x + 2 } \text { and } g ( x ) = 8 x - 6 \text {, find } ( f \circ g ) ( x )$

A study in a small town showed that the percent of residents who have college degrees can be modeled by the function $P = 32 x ^ { 0.31 }$ of years from 2015 . , where x is the number of years from 2010 . Rewrite the model with x equal to the number

Find the specified domain and express it in interval notation. -If f(x)=x-5 and g(x)=x-1 , evaluate (f+g)(2) .

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

Write the equation of the graph after the indicated transformation(s). -The graph of $y = x ^ { 2 }$ is shifted 4 units to the right. This graph is then vertically stretched by a factor of 6 and reflected across the $x$ -axis. Finally, the graph is shifted 8 units upward.

Find the specified domain and express it in interval notation. -If f(x)=x-7 and g(x)=-2 x²+13 x+2 , evaluate $( \mathrm { f } \cdot \mathrm { g } ) ( 5 )$ .