The graph of is reflected in different axes to obtain new curves.

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

The graph of

f(x)=\dfrac{1}{x}

is reflected in different axes to obtain new curves. (i) Write the algebraic expression of the image of

f

when it is reflected in the

x

–axis. Also state its domain and range. (ii) Write the algebraic expression of the image of

f

when it is reflected in the

y

–axis. Also state its domain and range. (iii) Sketch on the same coordinate plane the graphs of

f(x)

and the two reflections obtained in parts (i) and (ii). Mark the points where each graph meets the lines

x=\pm1

and

y=\pm1

. (iv) Compare and contrast the positions of the three graphs. Comment on how reflection in each axis changes the sign of

x

, the sign of

y

, and the quadrants in which the branches appear.