Exam 4: Polynomials and Rational Functions

Provide an appropriate response. -Explain the behavior of the graph of f(x) as it approaches its vertical asymptote. $f ( x ) = \frac { 5 } { ( x - 3 ) ^ { 2 } }$

Find all rational zeros and factor f(x). - $f ( x ) = 4 x ^ { 3 } - 28 x ^ { 2 } - x + 7$

The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction when the masses are 6 ft Apart?

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

Use synthetic division to perform the division. $\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }$

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - f ( x ) = - 2 x ^ { 4 } + 9 x ^ { 3 } - 7 x ^ { 2 } + 9 x - 7

The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 28 hours for 11 carpenters to frame a house, then how long will it take 49 carpenters to do the same job?

Provide an appropriate response. -Find a quadratic function $f$ having $x$ -intercepts 3 and $- 4$ and $y$ -intercept $- 24$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. Zero of -2 having multiplicity 2 and zero of 4 having multiplicity 1 ; P(0)=-16

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. - $f ( x ) = 2 x ^ { 4 } - x ^ { 3 } - 15 x ^ { 2 } + 3 x ; \quad k = - 3$

Find the domain and range of the function. - $f ( x ) = ( x + 3 ) ^ { 2 } + 8$

Determine which of the rational functions given below has the following feature(s). -The x-axis is its horizontal asymptote

Determine which of the rational functions given below has the following feature(s). - $x$ -intercepts: $( - 1,0 )$ and $( - 2,0 ) , y$ -intercepts: $\left( 0 , \frac { 2 } { 25 } \right)$ , vertical asymptote: $x = 5$ , horizontal asymptote: $y = 1$

Sketch the graph of the rational function. - $f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 }$

Find the equation that the given graph represents. -

Graph the polynomial function. Factor first if the expression is not in factored form. -

Graph the polynomial function. Factor first if the expression is not in factored form. - $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 7 x + 3$

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

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 40 x - 192$

Solve the problem. Round your answer to two decimal places. -Hooke's Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 15 pounds stretches a certain spring 9 inches, then how much will a force Of 30 pounds stretch the spring?