Transformation: Given the function f(x) = 4x3 - 2x +
7, find each of the following. Then discuss how each expression
differs from the other.
a) f(x) + 2
b) f (x + 2)
c) f(x) + f (2)
Unit 6 DQ Follow-up #1: Variation
Unit 6 DQ Follow-up # 1 question: If y varies directly as ,
explain why doubling x would not cause y to be doubled as well.
Unit 6 DQ Follow-up #2: Variation
Unit 6 DQ1...
For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the
following, and use it to graph the function.
Find: a)(2pts) Domain
b)(2pts) Intercepts
c)(2pts) Symmetry
d) (2pts) Asymptotes
e)(4pts) Intervals of Increase or decrease
f) (2pts) Local maximum and local minimum values
g)(4pts) Concavity and Points of inflection and
h)(2pts) Sketch the curve
For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find the
following, and use it to graph the function.
Find: a)(2pts) Domain
b)(2pts) Intercepts
c)(2pts) Symmetry
d) (2pts) Asymptotes
e)(4pts) Intervals of Increase or decrease
f) (2pts) Local maximum and local minimum values
g)(4pts) Concavity and Points of inflection and
h)(2pts) Sketch the curve
a. For the following probability density
function:
f(X)=
3/4 (2X-X^2 ) 0 ≤ X ≤ 2
=
0 otherwise
find
its expectation and variance.
b. The two regression lines are 2X - 3Y + 6 = 0 and 4Y – 5X- 8
=0 , compute mean of X and mean of Y. Find correlation coefficient
r , estimate y for x =3 and x for y = 3.
f(x,y) = 2/7(2x + 5y) for 0 < x < 1, 0 < y < 1
given X is the number of students who get an A on test 1
given Y is the number of students who get an A on test 2
find the probability that more then 90% students got an A test 2
given that 85 % got an A on test 1
5. Consider the function f(x) = -x^3 + 2x^2 + 2.
(a) Find the domain of the function and all its x and y
intercepts.
(b) Is the function even or odd or neither?
(c) Find the critical points, all local extreme values of f, and
the intervals on which f is increasing or decreasing.
(d) Find the intervals where f is concave up or concave down and
all inflection points.
(e) Use the information you have found to sketch...
Analyze the function given by f(x) = (2x − x^2 )e^x . That is:
find all x- and y-intercepts; find and classify all critical
points; find all inflection points; determine the concavity; find
any horizontal or vertical asymptotes. Finally, use this
information to graph the function.