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

$$f(x)=\frac{3x^2+x-5}{x^2+1}$$

Sketch the graph of $y=x^n$ and each transformation.

$$y=x^4$$

$\quad$ (a) $f(x)=(x+3)^4$

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

(c ) $h(x)=\left(\frac{1}{3}x\right)^2-3$

Find all the zeros of the function.

$$f(x)=\left(x+6\right)\left(x+i\right)\left(x-i\right)$$

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

(b) $g(x)=(3x)^2+1$

Find all the rational zeros of the function.

$$f(x)=x^3-6x^2+11x-6$$

Use long division to divide.

$$(x^3+4x^2-3x-12)\div(x-3)$$

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

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

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

$$f(x)=\frac{3x^2+1}{x^2+x+9}$$

Sketch the graph of $y=x^n$ and each transformation.

$y=x^5$ $\quad$ (d) $f(x)=-\frac{1}{2}(x+1)^5$

Sketch the graph of $y=x^n$ and each transformation.

$$y=x^5$$

$\quad$ (c) $f(x)=1-\frac{1}{2}x^5$

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

$$f(x)=\frac{2x^2-5x-12}{x^2-16}$$

Sketch the graph of $y=x^n$ and each transformation.

$y=x^5$ $\quad$ (b) $f(x)=x^5+1$

Write the complex number in standard form.

$$-10i+i^2$$