Graphs and transformations

Question code: 2A57

Question 0305

Write

y = \frac{ - x - 2 }{ x + 7 }

in the form

y = A + \frac{B}{x + 7}

and describe a sequence of transformations which transform the graph of

y = \frac{ - x - 2 }{ x + 7 }

to the graph of

y = \frac{ 1 }{ x }.

Sketch the graph of

y = \frac{ - x - 2 }{ x + 7 },

giving the equations of any asymptotes and the coordinates of any axial intercepts.

Answer

{y = -1 + \frac{ 5 }{ x + 7 }}

Transformation 1: Translate by 1 units in the positive

{y}

-axis direction.
Transformation 2: Scale by a factor of

{\frac{1}{5}}

parallel to the

{y}

-axis.
Transformation 3: Translate by 7 units in the positive

{x}

-axis direction.

Question code: 2A57