Answer:
See below.
Step-by-step explanation:
When x = 2 the denominator x - 2 is zero so there will be a vertical asymptote x = 2. When x approaches negative infinity the function will approach x axis from above and for positive infinity the graph will approach x-axis from below , so the horizontal asymptote is the x axis.
You can plot the following points on the the 2 parts of the graph:
(0, 1) and (-10, 0.2) on the left
(4, -1) and (2.2, -10) on the right
Drawing the graph:
First draw the vertical asymptote x = 2 ( a vertical line passing through the point (2, 0) on the x-axis.
Then starting on the left draw a line through (-10, 0.2) just above the x axis and continue to curve upwards through the point (0, 1) on the y axis, then continue sharply upwards to get close to but not to touch the vertical asymptote.
On the right of the y axis draw a line through the point (2.2 , -10) and curving upwards through the point (4, -1) then it goes close to the x axis but not touching it.
