Determine the domain, range, and vertical asymptote.Graph f(x)=-6-Inx
start with the parent graph of
y = ln x, which you should know how to sketch
Now graph y = -lnx, which would be a reflection in the x-axis
now drop that graph 6 units down to get
y = -lnx - 6
You should be able to answer your questions from that sketch.
First I have to figure out the domain,rande and vertical asymptotes
we can take logs of only positive numbers, so
- domain: x>0
- range: y is any real number
- no asymptotes
Thx! could u help me with graphing this
I described it for you in my reply above
The other option is to calculate about 8-10 ordered pairs and determine the sketch
e.g. (1, -6), (2, -6.7), (5, -7.6) , (.5, -5.3), (.01, -10.6) etc.
To determine the domain, range, and vertical asymptote of the function f(x) = -6 - ln(x), we can break down each concept separately:
1. Domain:
The domain of a function refers to the set of all possible input values (x-values) for the function. In this case, since we have ln(x) in the function, the natural logarithm function is only defined for positive values of x. Therefore, the domain of f(x) is all positive real numbers excluding zero. We can express this mathematically as:
Domain: x > 0
2. Range:
The range of a function corresponds to the set of all possible output values (y-values) that the function can attain. By examining the given function, we can see that the graph shifts the logarithm function downward by 6 units and reflects it across the x-axis. The natural logarithm function has a range of all real numbers, so when we shift it downward by 6 units, the range of f(x) is:
Range: y < -6
3. Vertical Asymptote:
A vertical asymptote is a vertical line that the graph of a function approaches but never crosses. To find the vertical asymptote, we examine the behavior of the function as x approaches values near zero. In this case, as x approaches zero from the positive side, the value of ln(x) increases without bound, resulting in f(x) decreasing without bound as well.
Therefore, the vertical asymptote is the line x = 0.
In summary:
Domain: x > 0
Range: y < -6
Vertical Asymptote: x = 0
To graph the function f(x) = -6 - ln(x), plot points on the graph based on different x-values within the specified domain, and connect them with a smooth curve.