5. Trazar las gráficas de las siguientes funciones, determinando dominio \( y \) \( \begin{array}{llll}\text { a. } F(x)=x^{2}-2 x & \text { b. } F(x)=-x^{2}-2 x & \text { c. } F(x)=x^{2}-2 x+2 & \text { d. } f(x)=\sqrt{x^{2}-2 x} \\ \text { e. } f(x)=\sqrt{-x^{2}-2 x} & \text { f. } F(x)=\left|x^{2}-2 x\right| & \text { g. } F(x)=\left|-x^{2}-2 x\right|\end{array} \)

(a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)=\sqrt{\mathrm{x}^{4}-3 \mathrm{x}^{2}+4} \) (Simplify your answer. Type an exact answer, using radicals as needed.) (b) What is \( d \) if \( x=0 \) ? If \( x=0 \), the distance \( d \) is (Type an integer or decimal rounded to two decimal places as needed.)

Given the function with the equation \( k(x)=\frac{-6}{x+2}-2 \) : \( 7.1 \quad \) Write the equations of the asymptotes of \( k \).

Given: \( f(x)=2\left(x^{2}-1\right) \) Sketch function \( f \) on the diagram sheet. Clearly show all intercepts with the axes.

Complete the sentence below. Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(-x) \) may be obtained by a reflection about the -axis of the graph of the function \( y=f(x) \). Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(-x) \) may be obtained by a reflection about the -axis of the graph of the function \( y=f(x) \).

Clearly indicate all intercepts with the axes as well as the QUESTION 7 Given the function with the equation \( k(x)=\frac{-6}{x+2}-2 \) : 7.1 Write the equations of the asymptotes of \( k \). 7.2 Give the range of \( k \). 7.3 Give the domain of \( k \).