SOLUTION: Hello! I need help with this equation. f(x)= 1/x-6 I need to find the domain, x-intercept and y=intercept,vertical and horizontal asymptote and the graph. Please explain

Question 977095: Hello!
I need help with this equation.
f(x)= 1/x-6
I need to find the domain, x-intercept and y=intercept,vertical and horizontal asymptote and the graph.
Please explain each step.
Thank you
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
As given in plain text, f(x)= 1/x-6

Rendering the function,

DOMAIN: The one value of x not acceptable is x=0.
The domain is all real numbers so that .

The undefined x at 0 gives a vertical asymptote at x=0.

f seems to approach -6 when x goes unbounded in either direction.
The rational term approaches 0, making the result easy to see or visualize.
Horizontal asymptote, y=-6.

NO VERTICAL AXIS INTERCEPT. Review the discussion given earlier.

What do you find if y=0?

---because the denominator does not control any of this.

------the x-axis intercept.

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
f(x)= 1/x-6
I need to find the domain, x-intercept and y=intercept,vertical and horizontal asymptote and the graph.
Please explain each step.
***
f(x)= 1/(x-6)
note: please use parenthesis as shown next time.(I assume this is what you meant)
..
Domain: all real numbers except x≠6. At x=6, denominator =0, making the function undefined.
x-intercept: none . Because of constant 1 in numerator, y≠0
y-intercept: -1/6
set x=0, then solve for y
Vertical asymptote: x=6
set denominator=0, then solve for x
horizontal asymptote: x-axis
rule: if power of x in numerator is less than power of x in the denominator, horizontal asymptote=x-axis or y=0
see graph below:

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