Use long division to divide.

$(x^4-5x^3+6x^2-x-2)\div(x+2)$

Use the Rational Zero Test to list all possible rational zeros of $f(x)=4x^5-8x^4-5x^3+10x^2+x-2$. Verify that the zeros of f shown on the graph are continued in the list.

Graph each function. Compare the graph of each function with the graph of $y=x^2$.

(d) $k(x)=x^2-3$

Graph each function. Compare the graph of each function with the graph of $y=x^2$.

(c ) $h(x)=x^2+3$

Write the complex number in standard form.

$\sqrt{-0.09}$

Graph each function. Compare the graph of each function with the graph of $y=x^2$.

(b) $g(x)=x^2-1$

Graph each function. Compare the graph of each function with the graph of $y=x^2$.

(a) $f(x)=x^2+1$

Write the complex number in standard form.

$$14$$

Find the domain of the function and identify any vertical and horizontal asymptotes.

$$f(x)=\frac{4x^2}{x+2}$$

Identify any intercepts and asymptotes of the graph of the function. Then sketch a graph of the function.

$$h(x)=\frac{4}{x^2}-1$$

Write the quadratic function in standard form and sketch its graph. Identify the vertex, axis of symmetry, and $x$-intercept(s).

$$f(x)=\frac{1}{2}\left(6x^2-24x+22\right)$$

Graph each function. Compare the graph of each function with the graph of $y=x^2$.

(d) $k(x)=-3x^2$

Use long division to divide.

$14$. $(6x^3-16x^2+17x-6)\div(3x-2)$

Average Cost A business has a production cost of $C=0.5x+500$ for producing $x$ units of a product. The average cost per unit $C$, is given by

$$\overline{C}=\frac{C}{x}=\frac{0.5x+500}{x}, \quad x\gt0.$$

Determine the average cost per unit as $x$ increases without bound. (Find the horizontal asymptote.)