Exam 10: Characteristics of Functions and Their Graphs

Use the Intermediate Value Theorem to determine if a real zero of f(x)occurs in the given interval. If this cannot be determined, indicate so. - $f ( x ) = - x ^ { 3 } - 6 x ^ { 2 } + 2 x + 5 \text { in } ( 5,6 )$

Graph the polynomial function. - $f ( x ) = 2 x ^ { 3 } - x ^ { 2 } - 18 x + 9$

Find all the rational zeros of the function. - $f ( x ) = 6 x ^ { 4 } + 13 x ^ { 3 } - 8 x ^ { 2 } - 17 x + 6$

Find the x-intercepts of the function. - $f ( x ) = ( x + 1 ) ( x - 2 ) \left( x ^ { 2 } - 9 \right)$

Determine the minimum degree of the polynomial function graphed. - $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 6 x$

List the possible rational zeros of the function. - $f ( x ) = 5 x ^ { 4 } - x ^ { 2 } + 3$

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - $f ( x ) = \frac { 5 } { x + 5 }$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = ( x + 1 ) ( x - 4 ) \left( x ^ { 2 } - 4 \right)$

Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give the equation of the asymptote if it exists. - $f ( x ) = \frac { 2 } { x - 1 }$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 2 } + 10 x + 21$

Classify the function as continuous or discontinuous. -

Classify the function as continuous or discontinuous. -

Find all the zeros (real and complex)of the function. - $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 17 x - 13$

Find the x-intercepts of the function. - $f ( x ) = x ^ { 2 } - 64$

Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial function. - $f ( x ) = 3 x ^ { 6 } - 9 x ^ { 5 } + x ^ { 4 } - 1.5 x ^ { 3 } + 18$

Use the Intermediate Value Theorem to determine if a real zero of f(x)occurs in the given interval. If this cannot be determined, indicate so. - $f ( x ) = 5 x ^ { 2 } - 3 x - 7 \text { in } ( 3,4 )$

Graph the piecewise function. - $g ( x ) = \left\{ \begin{array} { l l } 5 x + 5 & \text { if } x \leq 1 \\- \frac { 1 } { 5 } x + \frac { 6 } { 5 } & \text { if } x > 1\end{array} \right.$

Determine whether the function is an even function, an odd function, or neither. - $f ( x ) = x ^ { 3 } - 4 x$

Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give the equation of the asymptote if it exists. - $f ( x ) = \frac { x ^ { 2 } + 4 x - 6 } { x - 2 }$

Graph the rational function. - $f ( x ) = \frac { x ^ { 2 } + 6 x + 8 } { x + 5 }$