Given the functions
(a) f(x) = x³ + 5x² + x
(b) f(x) = x² + x
(c) f(x) = -x
Function (a)
f(-x) = (-x)³ + 5(-x)² + (-x)
= -x³ + 5x² - x
= -(x³ - 5x² + x)
The function is neither even nor odd.
Function (b)
f(-x) = (-x)² + (-x)
= -(-x² + x)
The function is neither even nor odd.
Function (c)
f(-x) = -(-x)
= x
= -f(x)
Because f(-x) = -f(x) the function is odd.
Answer: f(x) = -x is an odd function.
Answer:
v=3i+8j
Step-by-step explanation:
The given the vector v has an initial point (-2,-6) and a terminal point of (1,2).
To find the components of vector v, we subtract the terminal points from the initial point to obtain.
v=<1,2>-<-2,-6>
v=<1--2,2--6>
v=<1+2,2+6>
v=<3,8>
As a linear combination of the standard unit vectors.
v=3i+8j
Answer:
2
Step-by-step explanation:
The average rate of change from x=1 to x=2 is the same as finding the slope of a line at x=1 and x=2.
So we are going to need to corresponding y coordinates.
What y corresponds to x=1? y=3
What y corresponds to x=2? y=5
So we have the ordered pairs (1,3) and (2,5).
Line the points up vertically and subtract vertically then put 2nd difference over 1st difference.
(2 , 5)
-(1 , 3)
-----------
1 2
The average rate of change is 2/1 or just 2.
Now since we were asked to find the average rate of change given the function was a line, it really didn't matter what two points you used on that line.
By applying the definition of continuity and knowing piecewise functions, we know that the solution to this system of linear equations is c = 10 and d = -8.
<h3>How to make a piecewise function continuous</h3>
According to the <em>functional</em> theory, functions are continuous for a given interval if and only if the function has an only value for each element of the interval. In the case of the <em>piecewise</em> function, we must observe these two conditions:
2 · x = c · x² + d, for x = 1 (1)
4 · x³ = c · x² + d, for x = 2 (2)
Then, we have the following system of linear equations:
c + d = 2 (1b)
4 · c + d = 32 (2b)
The solution to this system of linear equations is c = 10 and d = -8.
To learn more on piecewise functions: brainly.com/question/12561612
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Answer:
y=4/1x+-3
Step-by-step explanation:
I hope this helps...
