Exam 4: Additional Topics With Functions

Find the specified domain and express it in interval notation. -If f(x)=5 x-7 and g(x)=3 x²+14 x+2 , evaluate $\left( \frac { \mathrm { f } } { \mathrm { g } } \right)$ (-4)

Determine whether or not the function is one-to-one. - $f ( x ) = x ^ { 3 } + 5$

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f(x)=|x| ; g(x)=-4|x|$

Use the given graph of f(x) $f ( x ) = a x ^ { 2 } + b x + c$ c to solve the specified inequality. - $f(x)<0$

Solve the equation - $\sqrt [ 3 ] { 3 x + 7 } = - 2$

Use the given graph of f(x) $f ( x ) = a x ^ { 2 } + b x + c$ c to solve the specified inequality. - $f(x) \geq 0$

Find the specified domain and express it in interval notation. -For $f ( x ) = x ^ { 2 } - 9$ and $g ( x ) = 2 x + 3$ , what is the domain of $\left( \frac { f } { g } \right) ( x )$ ?

Find the requested composition of functions. -Given $f ( x ) = 5 x + 9$ and $g ( x ) = 4 x - 1$ , find $( f \circ g ) ( x )$ .

For the pair of functions, perform the indicated operation. - $f ( x ) = x ^ { 2 } + 1 , g ( x ) = 2 x - 7 \quad \text { Find } ( f \cdot g ) ( x )$

Write the equation of the graph after the indicated transformation(s). -The graph of $y = x ^ { 2 }$ is vertically stretched by a factor of 2 , and the resulting graph is reflected across the $x$ -axis.

Use the quadratic formula or graphing methods to - $9 x ^ { 2 } \leq 3 - 3 x$

Find the requested composition of functions. -Given $f ( x ) = \frac { 5 } { x - 8 }$ and $g ( x ) = \frac { 4 } { 5 x }$ , find $( f \circ g ) ( x )$

The year y when sales were s million dollars for a particular electronics company can be modeled by the radical equation $y = 1.4 \sqrt { s - 2 } - 7$ , where $y = 1$ represents 2010 , and so on. Use the model to predict the sales for 2015 to the nearest tenth of a million.

Determine whether or not the function is one-to-one. - $f ( x ) = 8 x + 7$

Solve the equation - $\sqrt { 2 x ^ { 2 } + 42 } = \sqrt { x ^ { 2 } + 13 x }$

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. -

Determine if the function f defined by the arrow diagram has an inverse. If it does, create an arrow diagram that defines the inverse. If not, explain why not. -

Determine whether or not the function is one-to-one. - $\{ ( 6 , - 5 ) , ( 8 , - 15 ) , ( 11 , - 10 ) , ( 19 , - 19 ) , ( 22 , - 23 ) \}$

For the pair of functions, perform the indicated operation. - $f ( x ) = 7 - 8 x , g ( x ) = - 4 x + 8 \quad$ Find $( f + g ) ( x )$

Fill in each blank with the appropriate response. -The graph of $y = - 3 x ^ { 2 }$ can be obtained from the graph of $y = x ^ { 2 }$ by vertically stretching by a factor ofــــــــ and reflecting across the ــــــــــ-axis.