Josephood7

Consider the graph of the function f(x)=−2x2+5x−12x−1f(x)=−2x2+5x−12x−1

A. What is the y-intercept of the graph? yy = 

For the following 3 questions, enter all possible values, separated by commas. If there are none, type 'none'.

B. What are the x-intercepts of the graph? xx =

C. At what values of xx does the graph have a vertical asymptote? xx = 

D. At what values of yy does the graph have a horizontal asymptote? yy =

E. What is the equation of the slant asymptote with the highest slope? yy =

For the following 2 questions, enter your answers in the form (-2, 3], (-I,0)U[1,2), etc. using I for ∞∞ or type 'empty' for ∅∅

F. For what values of xx is ff decreasing? 

G. For what values of xx is ff concave up?

Consider the graph of the function f(x)=ex−8xf(x)=ex−8x

A. What is the y-intercept of the graph? yy = 

B. How many x-intercepts are there? There are  x-intercepts

For the following question, enter all possible values, separated by commas. If there are none, type 'none'.

C. At what values of xx does the graph have a vertical asymptote? xx = 

D. What is the equation of the slant asymptote with the highest slope? yy =

For the following 2 questions, enter your answers in the form (-2, 3], (-I,0)U[1,2), etc. using I for ∞∞ or type 'empty' for ∅∅

E. For what values of xx is ff decreasing? 

F. For what values of xx is ff concave up? 

Consider the graph of the function f(x)=x2+4x−−−−−−√f(x)=x2+4x

For the following question, enter your answers in the form (-2, 3], (-I,0)U[1,2), etc. using I for ∞∞ or type 'empty' for ∅∅

A. What is the domain of the function? 

B. What is the y-intercept of the graph? yy = 

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? xx = 

D. At what values of xx does the graph have a vertical asymptote? xx = 

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 x2+4x−−−−−−√−(mx+b)x2+4x−(mx+b) it helps to multiply by the expression x2+4x√+(mx+b)x2+4x√+(mx+b)=1x2+4x+(mx+b)x2+4x+(mx+b)=1 and then choose mm and bb 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)U[1,2), etc. using I for ∞∞ or type 'empty' for ∅∅

F. For what values of xx is ff decreasing? 

G. For what values of xx is ff concave up? 

Suppose that

(A) Find all critical values of ff. If there are no critical values, enter None . If there are more than one, enter them separated by commas.
Critical value(s) = 

(B) Use interval notation to indicate where f(x)f(x) is increasing.

Note: When using interval notation in WeBWorK, you use I for ∞∞, -I for −∞−∞, and U for the union symbol. If there are no values that satisfy the required condition, then enter "{}" without the quotation marks.

Increasing:

(C) Use interval notation to indicate where f(x)f(x) is decreasing.
Decreasing:

(D) Find the xx-coordinates of all local maxima of ff. If there are no local maxima, enter None . If there are more than one, enter them separated by commas.

Local maxima at xx = 

(E) Find the xx-coordinates of all local minima of ff. If there are no local minima, enter None . If there are more than one, enter them separated by commas.

Local minima at xx = 

(F) Use interval notation to indicate where f(x)f(x) is concave up.
Concave up:

(G) Use interval notation to indicate where f(x)f(x) is concave down.
Concave down:

(H) Find all inflection points of ff. If there are no inflection points, enter None . If there are more than one, enter them separated by commas.
Inflection point(s) at xx = 

(I) Use all of the preceding information to sketch a graph of ff. When you're finished, enter a 1 in the box below.

Graph Complete: