Exam 3: Polynomial and Rational Functions

Use the graph of the rational function shown to complete the statement. - As $x \rightarrow - 2 ^ { - } , f ( x ) \rightarrow ?$

Choose the one alternative that best completes the statement or answers the question. Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = - 6 x + 5 + x ^ { 2 }$

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - $f ( x ) = x ^ { 4 } + 3 x ^ { 3 } - 18 x ^ { 2 } - 36 x - 16$

x Find the range of the quadratic function. - $f ( x ) = - 3 x ^ { 2 } + 3 x$

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. - $f ( x ) = 7 x ^ { 4 } - 8 x ^ { 3 } + x ^ { 2 } - 3.5 x + 16$

Use the graph of the rational function shown to complete the statement. - As $\mathrm { x } \rightarrow - 2 ^ { - } , \mathrm { f } ( \mathrm { x } ) \rightarrow$ ?

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - $x ^ { 2 } - 2 x - 3 \leq 0$

Graph the rational function. - $f ( x ) = \frac { x ^ { 2 } - x - 20 } { x ^ { 2 } - 1 }$

Find the domain of the rational function. - $g ( x ) = \frac { x + 9 } { x ^ { 2 } + 1 }$

Choose the one alternative that best completes the statement or answers the question. Use the vertex and intercepts to sketch the graph of the quadratic function. - $f(x)=4(x+4)^{2}+6$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = 4 x ^ { 4 } - 3 x ^ { 2 }$

Determine the maximum possible number of turning points for the graph of the function. -Suppose that a polynomial function is used to model the data shown in the graph below. For what intervals is the function increasing?

Solve the problem. -In one U.S. city, the quadratic function $f ( x ) = 0.0037 x ^ { 2 } - 0.48 x + 36.78$ models the median, or average, age, $y$ , at which men were first married x years after 1900 . In which year was this average age at a minimum? (Round to the nearest year.) What was the average age at first marriage for that year? (Round to the nearest tenth.)

Choose the one alternative that best completes the statement or answers the question. Use the vertex and intercepts to sketch the graph of the quadratic function. - $y-3=(x+5)^{2}$

Find an nth degree polynomial function with real coefficients satisfying the given conditions. - $\mathrm { n } = 4 ; 3 , \frac { 1 } { 2 }$ , and $1 + 3 \mathrm { i }$ are zeros; $\mathrm { f } ( 1 ) = - 54$

Solve the problem. -The owner of a video store has determined that the profits $\mathrm { P }$ of the store are approximately given by $P ( x ) = - x ^ { 2 } + 150 x + 71$ , where $x$ is the number of videos rented daily. Find the maximum profit to the nearest dollar.

Determine whether the graph shown is the graph of a polynomial function. -

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = ( x + 9 ) ^ { 2 } - 2$

x Find the range of the quadratic function. - $f ( x ) = 11 ( x - 3 ) ^ { 2 } + 7$

Determine whether the graph shown is the graph of a polynomial function. -