Exam 4: Polynomials and Rational Functions

Sketch the graph of the rational function. - $f ( x ) = \frac { x + 2 } { x ^ { 2 } - 9 }$

Suppose a cost-benefit model is given by f(x) $f ( x ) = \frac { 3.9 x } { 100 - x }$ , where y is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 30% to the nearest dollar.

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

Find an equation for a rational function with the following asymptotes: vertical asymptote $x = 3$ , horizontal asymptote $y = - 6$

If a rocket is propelled upward from ground level, its height in meters after t seconds is given by $h ( t ) = - 9.8 t ^ { 2 } + 49 t$ During what interval of time will the rocket be higher than 58.8m ?

What are the possible number of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree four?

Determine whether the statement is true or false. - $f(x)=\frac{7}{x^{2}}$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 1 } { ( x + 4 ) ^ { 2 } }$

Find all rational zeros and factor f(x). $f ( x ) = 6 x ^ { 3 } + 19 x ^ { 2 } + 8 x - 5$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$ -intercepts?

The graph of $f ( x ) = x ^ { 4 } + x ^ { 3 } - 6 x ^ { 2 } - x ^ { 2 } - x + 6$ is shown below. Use the graph to factor $f ( x )$ .

Sketch the graph of the parabola. - $y=-x^{2}-2$

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. -

How can the graph of $f ( x ) = - \frac { 6 } { x }$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = 3 ; f ( x ) = - 7 x ^ { 3 } + x ^ { 2 } - 2 x + 8$

Determine whether the statement is true or false. - $f ( x ) = \frac { 1 } { ( x - 1 ) ^ { 2 } }$

The graph of $f ( x ) = x ^ { 3 } - x ^ { 2 } - 8 x + 12$ is shown below. Use the graph to factor $f ( x )$ .

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 37 x - 90 ; [ 2,3 ]$

Sketch the graph of the parabola. -

Find a quadratic function f having x-intercepts -9 and -2 and y-intercept 6