Exam 2: Functions and Relations

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given $g ( x ) = \sqrt { x - 5 }$ the domain is restricted so that $x \geq$ .

Evaluate the function for the indicated value. -Evaluate $f ( 10 )$ $f ( x ) = \left\{ \begin{array} { c c } 9 & x \leq - 1 \\| x + 1 | & - 1 < x \leq 2 \\- 2 & x > 2\end{array} \right.$

Write the domain in interval notation. - $f ( x ) = \frac { x + 7 } { x + 3 }$

Write an equation of the line satisfying the given conditions. Write the answer in standard form with no fractional coefficients. -Passes through $( - 1 , - 4 )$ and is parallel to the line defined by $5 x + 3 y = - 8$

Compute the least-squares regression line for predicting the ribeye price from the corn price. -One of the primary feeds for beef cattle is corn. The following table presents the average price in dollars for a bushel of corn and a pound of ribeye steak for 10 consecutive months. Corn Price (\ /) Ribeye Price (\ /) 6.67 14.42 5.75 11.90 6.06 12.35 5.92 12.62 6.36 13.01 6.13 13.27

Solve the problem. -If the slope of a line is $\frac { 7 } { 10 }$ , how much vertical change will be present for a horizontal change of $63 \mathrm { ft }$ ?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - $x = y ^ { 2 } + 6$

Determine the x- and y-intercepts for the given function. - $f ( x ) = \sqrt { x } - 2$

Evaluate the function for the indicated value, then simplify. - $f ( x ) = 2 x ^ { 2 } - 4 x ;$ find $f ( 8 )$

Evaluate the function for the given value of x. - $g ( x ) = \sqrt { 3 x } , h ( x ) = x ^ { 3 } + 5 x , ( g \circ h ) ( 2 ) = \text { ? }$

Write the word or phrase that best completes each statement or answers the question.Provide the missing information. -The function $\left( \frac { f } { g } \right) ( x )$ is defined by ــــــــــــprovided that ـــــــــــــــ $= 0 .$

Use the graph of y = f (x) to answer the questions. -a. Determine $f ( - 1 )$ b. Find all $x$ for which $f ( x ) = - 4$

Solve the problem. -If a plane loses 800 feet in altitude over a horizontal distance of 14,000 feet, what is the slope?

Write the equation in standard form: $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Then, if possible, identify the center and radius of the circle. If the equation represents a degenerate case, give the solution set. - $x ^ { 2 } + y ^ { 2 } + 4 x + 8 y + 11 = 0$

Evaluate the function for the given value of x. - $f ( x ) = x ^ { 2 } + 3 x , g ( x ) = 5 x + 2 , ( f \circ g ) ( 3 ) = ?$

Evaluate as indicated. -If $z ( t ) = 2 t ^ { 2 } + 7 t - 4$ , find $z ( - 1 )$ and $z ( 4 )$ .

Write the domain in interval notation. - $f ( x ) = \frac { x - 4 } { x - 5 }$

Graph the function by applying an appropriate reflection. - $f ( x ) = - \sqrt [ 3 ] { x }$

Determine whether the relation defines y as a function of x. -

Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant. -