How do you graph y=-5/x using asymptotes, intercepts, end behavior?

1 Answer
marfre
Jul 9, 2018

See answer below

Explanation:

Given: y = -5/x

This is called a rational function: (N(x))/(D(x)).

Find vertical asymptote(s):

When D(x) = 0 we have vertical asymptotes:

vertical asymptote at x = 0

End conditions:
The negative coefficient means the graph is reflected about the x-axis. So instead of starting in above the x-axis, the function starts below the x-axis.

Find y-intercept by setting x = 0:

y = -5/0 => y = undefined. " no "y-intercept

Find x-intercepts by setting y = 0: " "0 = -5/x

Multiply both sides by x: " "0 * x = -5, " "0 = -5 Not TRUE

This means there is no x-intercepts.

graph{-5/x [-10, 10, -10, 10]}

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