Exam 4: Polynomials and Rational Functions

Use synthetic division $f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$ for the given value of k. - $f ( x ) = 2 x ^ { 5 } - x ^ { 4 } + 3 x ^ { 2 } - x + 5 ; \quad k = 1$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=(-3 x-2)(x-2)^{2}$

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of $x ^ { 2 }$ should be positive or negative. -The height of a bouncing ball during one bounce, as a function of time.

If an object is thrown upward with an initial velocity of $96 \mathrm { ft } / \mathrm { sec }$ , its height after $\mathrm { t }$ sec is given by $s ( t ) = 96 \mathrm { t } - 16 \mathrm { t } ^ { 2 }$ . Find the maximum height attained by the object. (The object will attain maximum height exactly at the halfway point in terms of the time $t$ , where $t = 0$ is at the beginning of the object's flight, and the final time is when the object hits the ground.)

Determine which of the rational functions given below has the following feature(s). -The horizontal asymptote is $y = 5$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 1 } { x }$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } + 4 x - 12 < 0$

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = x ^ { 2 } - 3$

What type of variation is suggested by the graph?

Use synthetic division $f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$ for the given value of k. - $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 4 ; \quad k = 2$

Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a<0;-4ac>0

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 9$

Determine whether the statement is true or false. - $f ( x ) = \frac { 8 } { x }$

The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches, according to the equation $M ( x ) = 20 x - x ^ { 2 }$ . What rainfall produces the maximum number of mosquitoes?

Find a polynomial function f(x) of least possible degree having the graph shown. -

If an object is propelled upward from a height of 48 feet at an initial velocity of 64 feet per second, then its height after t seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 64 t + 48$ , where height is in feet. After how many Seconds will the object reach a height of 112 feet?

Why is it not possible for a function defined by a polynomial of degree 4 with real coefficients to have zeros of 2, $3,5 , \text { and } 1 + i$

Find a polynomial function f(x) of least possible degree having the graph shown. -