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URGENTLY PLEASE I WILL PUT A THUMBS UP Section A: Characteristics of Functions & Graphing Choose 1 (one) of the following questions to complete. (10 marks each) Given

`f(x)=(x)/(x^(2)-2x-15)=(x)/((x-5)(x+3))`

Determine the properties of

`f(x)`

and use this information to sketch a graph of the function. i) Domain & Range ii)

`x`

and

`y`

-intercepts iii) Vertical Asymptote(s) and Behavior at V.As: iv) Horizontal Asymptote and End Behavior: The function

`f(x)=log_(2)x`

is stretched vertically by a factor of 3 , reflected in the

`y`

-axis, translated right 2 units and down 5 units. Write the equation of the transformed function. State the mapping rule for the transformation in part (a). Map at least three points on the base function

`f(x)=log_(2)x`

to the points on the transformed function. Sketch a graph of the transformed function. Label any asymptote(s) on your graph. Determine the equation of the function with a leading coefficient of -1 , and zeros at 0 (order of 3 ), 3 (order of 1 ), -2 (order of 2 ). Sketch a graph of the function, clearly showing the behavior at the zeroes. State the intervals where

`f(x)>0`

. Sketch a cycle of the function

`f(x)=2sin((1)/(2)(x-(\pi )/(2)))+1`

. Determine properties of

`f(x)`

including: amplitude, period, phase shift, axis of the curve, domain, range, and key mapping points.