Domain/Range
The function is increasing on the interval:
(- ∞, -1) and (1, ∞)
The local maxima of the function are https://www.desmos.com/calculator/wyk81xspxd
Local max y=3 at x = -1 on the interval (-2,2)
The absolute maxima of the function is https://www.desmos.com/calculator/wyk81xspxd
None! (must specify the domain)
The function below is odd because:
It is symmetric about the origin
The absolute maxima of the function on the interval (-2,2) is:https://www.desmos.com/calculator/wyk81xspxd
Absolute max y=3 at x = -1 on the interval (-2,2)
The domain of the relation is:
https://www.desmos.com/calculator/gnrxuvqtd5?tour=restrictions
(-∞, 3]
The function is increasing on the interval (use set builder notation):
https://www.desmos.com/calculator/gnrxuvqtd5?tour=restrictions
{x | - ∞ < x < 2}
This function is neither even or odd because:
It is not symmetric about the y-axis or the origin
The local maxima of the function below is:
Does not exist
The absolute minima of the function is: https://www.desmos.com/calculator/gnrxuvqtd5?tour=restrictions
Does not exist
The range of this relation is:
https://www.desmos.com/calculator/gnrxuvqtd5?tour=restrictions
(-∞, 4]
The function is decreasing on the interval (use set builder notation):
{x| 2 < x < 3}
Show f(x) = x^2 is even, using the point x = -3
Remember f(x)=f(-x) if f is even
f(-3) =(-3)^2= 9
f(-(-3)=f(3)= (3)^2 = 9
The local minima of the function on the interval (-1,1) is: https://www.desmos.com/calculator/izudskx8aa
y = -0.414 at x=0.707
The absolute maximum of the function occurs at what point: https://www.desmos.com/calculator/gnrxuvqtd5?tour=restrictions
(2,4)
The domain and range of this function are:
Domain: All real numbers
Range: All integers {..., -3, -2, -1, 0, 1,2 ,3, ...}
The function/relation is increasing and decreasing on the intervals:
https://www.desmos.com/calculator/gnrxuvqtd5?tour=restrictions
Increasing (- ∞ ,2) and (2,3)
Decreasing (2,3)
Show that the function is even or odd use x= 1/4
Test: f(x)=f(-x) even; f(-x)=-f(x) odd
f(1/4) = (1/4)^3=1/64
f(-1/4)=(-1/4)^3= -1/64 (not even)
-f(1/4)= -(1/4)^3=-1/64 (odd)
The local maxima and minima of the function on the interval (0, 5):
https://www.desmos.com/calculator/gnrxuvqtd5?tour=restrictions
Local maximum: y=4, at x =2
Local minimum: y = -2.236 at x = 2
The absolute maxima and minima of the function:
https://www.desmos.com/calculator/gnrxuvqtd5?tour=restrictions
Absolute maxima at y = 4 for x=2
No absolute minima