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

(b) $g(x)=\left[\frac{1}{2}(x-1)\right]^2-3$

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

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

Write the complex number in standard form.

$-4i^2+2i$

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.

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 $y=x^2$.

(d) $k(x)=\left(x+3\right)^2$

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

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

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

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

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

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

Write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the given point.

Vertex: $(4,1)$; point: $(2,-1)$

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

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

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 $f(x)=2x^4-17x^3+35x^2+9x-45$. Verify that the zeros of f shown on the graph are continued in the list.

Write the complex number in standard form.

$$-10i+i^2$$