1. Transform the following equations to canonical forms a) \( x^{2}+4 x y+4 y^{2}-20 x+10 y-50=0 \) b) \( 3 x^{2}+10 x y+3 y^{2}-12 x-12 y+4=0 \) c) \( x^{2}+2 x y+y^{2}-4 x-4 y+3=0 \) d) \( 9 x^{2}+24 x y+16 y^{2}-126 x+82 y-59=0 \) e) \( 3 x^{2}-8 x y-3 y^{2}+10 x-13 y+8=0 \) f) \( 3 x^{2}-5 x y+6 y^{2}+11 x-17 y+13=0 \) g) \( 9 x^{2}+24 x y+16 y^{2}+34 x+62 y+47=0 \) h) \( x^{2}-4 x y+4 y^{2}-12 x-6 y-39=0 \)

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 \( y=f(x) \).

Given \( f(x)=\frac{-2}{x}-2 \), Answer the following questions: .1 Write down the equations of the asymptotes of \( f(x) \). 2 Draw a neat sketch graph of \( f(x) \), clearly indicate the asymptotes and the intercepts with the axes. .3 Write down the domain and range of \( f(x) \).

Find the function that is finally graphed after the following transformations are applied to the graph of \( y=\sqrt{x} \) in the order listed. (1) Shift up 7 units (2) Reflect about the \( x \)-axis (3) Reflect about the \( y \)-axis \( y= \)

(a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)=\sqrt{x^{4}-3 x^{2}+4} \) (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 2 . (Type an integer or decimal rounded to two decimal placels as needed.) (c) What is \( d \) if \( x=1 \) ? If \( x=1 \), the distance \( d \) is \( \square \). (Type an integer or decimal rounded to two decimal places as needed.)

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