Exam 3: Polynomial and Rational Functions

Write an equation that expresses the relationship. Use k as the constant of variation. -If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance, R. If the current is 300 milliamperes when the resistance is 4 ohms, find the current when the resistance is 24 ohms.

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = 3 ( x + 1 ) ( x + 7 ) ^ { 2 }$

Divide using long division. -Two people are 31 years old and 21 years old, respectively. In x years from now, their ages can be represented by $x + 31$ and $x + 21$ . Use long division to find the ratio of the older person's age to the younger person's age in $x$ years.

x Find the range of the quadratic function. - $y + 9 = ( x + 3 ) ^ { 2 }$

Use the graph or table to determine a solution of the equation. Use synthetic division to verify that this number is a solution of the equation. Then solve the polynomial equation. - $2 x ^ { 3 } + 11 x ^ { 2 } + 17 x + 6 = 0$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 4 - ( x + 3 ) ^ { 2 }$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end -The following table shows the number of DWI arrests in a county for the years $1994 - 1998$ , where 1 represents 1994, 2 represents 1995, and so on. This data can be approximated using the third-degree polynomial $\mathrm { T } ( \mathrm { x } ) = - 0.65 \mathrm { x } ^ { 3 } + 0.59 \mathrm { x } ^ { 2 } + 59.86 \mathrm { x } + 4832$ Use the Leading Coefficient Test to determine the end behavior to the right for the graph of T. Will this function be useful in modeling the number of DWI arrests over an extended period of time? Explain your answer.

Determine the constant of variation for the stated condition. -f varies jointly as $\mathrm { q } ^ { 2 }$ and $h$ , and $\mathrm { f } = - 54$ when $\mathrm { q } = 3$ and $\mathrm { h } = 3$ . Find $\mathrm { f }$ when $\mathrm { q } = 4$ and $\mathrm { h } = 5$ .

Find the y-intercept of the polynomial function. - $f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$

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. - $f ( x ) = x ^ { 2 } ( x - 2 ) ( x - 6 )$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $3 x ^ { 4 } + 23 x ^ { 3 } + 89 x ^ { 2 } + 167 x + 78 = 0$

Find the horizontal asymptote, if any, of the graph of the rational function. - $f ( x ) = \frac { 10 x } { 5 x ^ { 2 } + 1 }$

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

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. Determine the degree of the polynomial function of best fit and the sign of the leading coefficient.

Write an equation that expresses the relationship. Use k as the constant of variation. - $y = \frac { 1 } { 2 } \text { when } x = 14$

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. - $f ( x ) = 2 x ^ { 3 } - 8 x + 10$ ; between $- 3$ and $- 2$

x Find the range of the quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } + 9$

Solve the problem. -You drive 115 miles along a scenic highway and then take a 36 -mile bike ride. Your driving rate is 5 times your cycling rate. Suppose you have no more than a total of 4 hours for driving and cycling. Let $x$ represent your cycling rate in miles per hour. Use a rational inequality to determine the possible values of X.

Divide using synthetic division. - $\left( x ^ { 4 } + 625 \right) \div ( x - 5 )$

Write an equation that expresses the relationship. Use k as the constant of variation. -The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 36 ft from a light is 3.9 foot-candles, find the intensity on a screen 90 ft from the light.