1) 2
x^2-2x-3
Find) Domain
Range
Is This Continuous?
Local min/max
Vertical Asymptote
Horizontal Asymptote
X Intercepts
Y Intercepts
for function
Domain
Domain is the set of values of x for which function is defined.
The given function is not defined at x = -1 and x = 3
So, domain
Range
Range is f(x) values (or y values) you get, when you put these domain x values in function f(x). Since the function has a horizontal Asymptote at y = 0, so, y = 0 is excluded from Range.
So, Range
Horizontal Asymptote (HA)
To find HA, divide Numerator and denominator of the function with highest degree (power) of x. Then take limit
divide with highest degree, ,
Now take
HA is y = 0
Vertical Asymptote (VA)
For VA, Denominator = 0
(x+1)(x-3) = 0
x = -1 and x = 3
The graph is discontinuous at x = -1 and x = 3
y-intercepts
For y-intercept, put, x = 0 in equation,
we get, y = -2/3
y-intercept = -2/3, the graph cuts y-axis at -2/3.
x-intercepts
For x-intercept, put, y = 0 in equation,
we do not get any answer from this, so there is no, x-intercept. i.e., the graph does not cuts x-axis
Please see attached graph, the green lines show the asymptotes.