Intro to Functions
What are all of the x-values in a function called?
Domain
Given the domain of f(x) is (3,5) U (9, infinity) and the domain of g(x) is (-1,4) U (7, 20), what is the domain of (f+g)(x)?
(3,4) U (9,20)
Without using the 3d graphing calculator, what do you think the equation z = cos(x)cos(y) looks like?
(Check the 3d Calculator) - Waves
Consider the functions y > x-2 and y < x. Give a point in the solution set and one point not in the solution set.
In Solution: (2,1)
Out of Solution: (1,4)
What is the magnitude of the vector <1,7>?
(50)^0.5
Describe the minima and maxima of the function: f(x) = x^{4}-4x^{3}+x^{2}+7x-3
Absolute minimum: (-0.629, -5.855)
Local Minimum: (2.529, -2.695)
Local Maximum: (1.1, 2.05)
No Absolute Maximum
What is g(f(x)) if f(x) = x-1 and g(x) = x^2?
g(f(x)) = x^2 - 2x +1
Please plot the point (1,2,3).
(Check the 3d Calculator)
Consider the inequalities y >= 2x and y <= 2x. What function describes the solution set to this system?
y = 2x
Boat A: <3,4> and Boat B: <2,-2>
If boat A starts at (1,1) and boat B starts at (5,-3), do the boat paths intersect? Do they collide?
Yes, they intersect.
No, they do not collide.
Describe the intervals on which the function cos((pi)x) is increasing and decreasing.
Decreasing: x ∈ (0+2n, 1+2n) where n ∈ (Z); Increasing: x ∈ (-1+2n, 0+2n) where n ∈ (Z)
Given that f(x) = 2x and g(x) = x+1, for which value of x is the function (f/g)(x) not defined?
x = -1
Please plot the set plane at z = 1 for the function z = 2x + 3y.
(Check Student Response)
Please describe the solution set to the following inequalities in set builder notation:
y > 4 and y >= x/2 + 1
{(x,y) | y > 4 when x ∈ (- infinity, 6)}
{(x,y) | y > x/2 + 1 when x ∈ (6, infinity)}
Transform the function y = |x| using the following list of transformations:
up by 2, left by 3, vertical stretch by a factor of 4, horizontal shrink by a factor of 3, reflect across y axis
y = 4|-3x+9| + 8
Please describe the function: f(x) = 2x^3 + 5x^2 -2
Domain: R; Range: R; Increasing: (- infinity, -5/3) U (0, infinity); Decreasin: (-5/3, 0); Local Max: (-5/3, 2.63); Local Min: (0,-2)
Find the Domain of f(g(x)) given: f(x) = x^2 +1 and g(x) = 3/x
Domain: (-infinity, 0) U (0, infinity)
Please plot the function (-z)^2 = x^2 + y^2 -1
Unit Sphere
Consider a solution set of inequalities lies between the points: (4,5), (3,2), and (1,3). Find the inequalities that this is the solution set for and describe this solution set in set builder notation. You may assume that all of the inequalities are solid lines.
Inequalities: (y-3) >= -1/2(x-1); (y-5) <= 2/3(x-4); (y-2) >= 3(x-3)
{(x,y) | -1/2(x-1) + 3 <= y <= 2/3(x-4) + 5 when x ∈ [1,3]}
{(x,y) | 3(x-3) + 2 <= y <= 2/3(x-4) + 5 when x ∈ (3,4]}
((8/(97)^.5)+2, 18/(97)^.5)-2)