Exam 3: Polynomial and Rational Functions

Determine the constant of variation for the stated condition. - $\mathrm { s }$ varies directly as $\mathrm { r } ^ { 2 }$ , and $\mathrm { s } = 80$ when $\mathrm { r } = 4$ .

Solve Combined Variation Problems - $p$ varies directly as $q$ and inversely as $r$ .

Write an equation that expresses the relationship. Use k as the constant of variation. -d varies directly as the square of $\mathrm { m }$ .

Determine the constant of variation for the stated condition. - $y$ varies jointly as a and $b$ and inversely as the square root of $c . y = 18$ when $a = 2 , b = 9$ , and $c = 16$ . Find $y$ when $a = 6 , b = 7$ , and $c = 25$ .

Graph the polynomial function. - $f ( x ) = x ( x + 1 ) ( x + 2 )$

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. - $\frac { 2 x } { x + 6 } < x$

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $f ( x ) = 5 x ^ { 2 } - x ^ { 3 }$

Solve Combined Variation Problems -w varies directly as a and inversely as the difference between $x$ and $y$ .

Solve the problem. -Among all pairs of numbers whose sum is 88 , find a pair whose product is as large as possible.

Determine whether the function is a polynomial function. - $f ( x ) = 7 - \frac { 2 } { x ^ { 5 } }$

Use transformations of f(x) $f ( x ) = \frac { 1 } { x } \text { or } f ( x ) = \frac { 1 } { x ^ { 2 } }$ to graph the rational function. - $f ( x ) = \frac { 1 } { x } - 2$

x Find the range of the quadratic function. - $f ( x ) = 4 x ^ { 2 } + 2 x - 6$