Exam 2: Polynomial, Power, and Rational Functions

Write the statement as a power function equation. Use k as the constant of variation. -The altitude $h$ of an equilateral triangle varies directly as one side s.

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. - $f ( x ) = - 9 x ^ { 3 } - 4 - 19 x ^ { 4 } + x ^ { 9 } + 14 x ^ { 2 }$

Solve the problem. -The first column shows the independent variable $( x )$ . The second column shows the dependent variable (y). Find the linear regression model.

Solve the problem. -The cost of producing $\mathrm { t }$ units is $\mathrm { C } = 4 \mathrm { t } ^ { 2 } + 8 \mathrm { t }$ , and the revenue generated from sales is $\mathrm { R } = 5 \mathrm { t } ^ { 2 } + \mathrm { t }$ . Determine the number of units to be sold in order to generate a profit.

Solve the problem. -A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of $176 \mathrm { ft } / \mathrm { sec }$ , and the gorge is $448 \mathrm { ft }$ deep, during what interval can the flare been? $\left( h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \right. \text { ) }$

Provide an appropriate response. -Suppose that $k , a , b$ , and $c$ are real numbers and that the polynomial function $f$ may be expressed in factored form as $f ( x ) = ( x - k ) \left( a x ^ { 2 } + b x + c \right)$ . If $b ^ { 2 } - 4 a c = - 57$ , determine the number of real and imaginary zeros that $f$ has.

Using the given zero, find all other zeros of f(x). -5 - $i$ is a zero of $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 35 x ^ { 2 } - 10 x + 34$ .

Write an equation for the quadratic function whose graph contains the given vertex and point. - (Write your answer in vertex form.)

Determine if the function is a monomial function (given that c and k represent constants). If it is, state the degree and leading coefficient. - $f ( x ) = - 5 \cdot 5 ^ { x }$

Match the equation to one of the curves (for x ≥ 0). - $f ( x ) = - 4 x ^ { - 2 }$

Determine whether the power function is even, odd, or neither. - $f ( x ) = 3 x ^ { 1 / 7 }$

Match the equation to one of the curves (for x ≥ 0). - $f ( x ) = - 3 x ^ { 5 / 3 }$

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - $f ( x ) = x ^ { 3 } - 7 x ^ { 2 } + 10 x + 6$

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. - $f ( x ) = \sqrt [ 3 ] { 64 x ^ { 9 } + 27 x ^ { 3 } }$

Graph the function in a viewing window that shows all of its extrema and x-intercepts. - $f ( x ) = 2 x ^ { 3 } + 2 x ^ { 2 } + 9 x - 8$

Solve the inequality. - $( x + 6 ) | x - 2 | \geq 0$

Solve the problem. -The length of a rectangle is 8 inches more than the width. The perimeter of the rectangle is 124 inches. Find the width of the rectangle.

For the given function, find all asymptotes of the type indicated (if there are any) - $f ( x ) = \frac { ( x - 5 ) ( x + 4 ) } { x ^ { 2 } - 9 }$ , vertical

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $x + 5 = \frac { 6 } { x }$

Graph the function. - $f(x)=(x-1)(x+3)^{4}$