(1 point) Consider the graph of the function
f(x)=\sqrt(x^(2)+4x)
For the following question, enter your answers in the form
(-2,3],(-I,0)\cup [1,2)
, etc. using I for
\infty
or type 'empty' for
(O)/()
A. What is the domain of the function? B. What is the y-intercept of the graph?
y=
For the following 2 questions, enter all possible values, separated by commas. If there are none, type 'none'. c. What are the x-intercepts of the graph?
x=
D. At what values of
x
does the graph have a vertical asymptote?
x=
E. What is the equation of a slant asymptote with positive slope?
y=
Hint: If you would like to understand an expression of the form
\sqrt(x^(2)+4x)-(mx+b)
it helps to multiply by the expression
(\sqrt(x^(2)+4x)+(mx+b))/(\sqrt(x^(2)+4x)+(mx+b))=1
and then choose
m
and
b
so that there is a large amount of cancellation in the numerator. For the following 2 questions, enter your answers in the form
(-2,3],(-I,0)\cup [1,2)
, etc. using I for
\infty
or type 'empty' for
(O)/()
F. For what values of
x
is
f
decreasing? G. For what values of
x
is
f
concave up?