Is the set (3,1),(6,4),(9,7),(12,10) a function? Explain how you know
How to take derivative of absolute value.
The absolute value function is defined as
[tex]|x| = \begin{cases}x & \text{for }x \ge 0 \\ -x & \text{for }x < 0\end{cases}[/tex]
If x is strictly positive (x > 0), then |x| = x, and d|x|/dx = dx/dx = 1.
If x is strictly negative (x < 0), then |x| = -x, and d|x|/dx = d(-x)/dx = -1.
But if x = 0, the derivative doesn't exist!
In order for the derivative of a function f(x) to exist at x = c, the limit
[tex]\displaystyle \lim_{x\to c}\frac{f(x) - f(c)}{x-c}[/tex]
must exist. This limit does not exist for f(x) = |x| and c = 0 because the value of the limit depends on which way x approaches 0.
If x approaches 0 from below (so x < 0), we have
[tex]\displaystyle \lim_{x\to 0^-}\frac{|x|}x = \lim_{x\to0^-}-\frac xx = -1[/tex]
whereas if x approaches 0 from above (so x > 0), we have
[tex]\displaystyle \lim_{x\to 0^+}\frac{|x|}x = \lim_{x\to0^+}\frac xx = 1[/tex]
But 1 ≠ -1, so the limit and hence derivative doesn't exist at x = 0.
Putting everything together, you can define the derivative of |x| as
[tex]\dfrac{d|x|}{dx} = \begin{cases}1 & \text{for } x > 0 \\ \text{unde fined} & \text{for }x = 0 \\ -1 & \text{for }x < 0 \end{cases}[/tex]
Help please please help me
Answer:
Hi! I hope this answer helps you.
In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x.
any vertical line in the plane can intersect the graph of a function at most once.
HOW TO DO THIS
take your pencil and place it on your paper vertically (up and down direction)
move the pencil across the paper to the right
if the pencil crosses more than two points on the line it is not a function
the first problem would be a function
the second problem would be a function
the third problem would not be a function
hope this helps !!!!
Solve the system of equations by substitution.
3/8x + 1/3y = 17/24
x + 7y = 8
6. Calculate the compound interest on investing $600.00 for 2 years at 7% per year.
Answer:
686.94
Step-by-step explanation:
first year, 42 interest
second year, 44.94 interest
Total=686.94
HELPPPPPPPPP
A: 5 units
B: 4 units
C: 3 units
D: 2 units
Answer:
Its 5 units why its simple X and Y is in a strait line which mean you measure it and divide it by 3.14 which is pie you get your answer.
Step-by-step explanation:
mark brain if im correct :D
Split £10 into the ratio 4:1
Answer:
let the shares be 4x and 1x (4:1)
total share = 4x + 1x = 5x
total amount = 10£
5x = 10£
x = 2£
1st share = 4x = 4*2£ = 8£
2nd share = 1x = 1*2£ = 2£
.
.
[tex]{\bold{\red{HOPE\:IT\:HELPS!}}}[/tex]
[tex]\color{yellow}\boxed{\colorbox{black}{MARK\: BRAINLIEST!❤}}[/tex]
Solve inequality 5x+ 3 divided by 2 > 3x+2
Step-by-step explanation:
divide 3÷2 (5x+1.5>3x+2)
move the terms (5x-3x>2-1.5)
2x>0.5
divide by 2
x=0.25
How to tell if a piecewise function is differentiable.
Answer:
So what we're going to do is now take the so drdx of negative 3x plus 1 is equal drdx of x squared
Step-by-step explanation:
Did I do this correctly? (please help asap will mark brainliest)
Answer:
Ooh that is incorrect try again.
What is between 8.79 and 8.80 on a numberline
Answer:
8.795 is exactly half way between them
Step-by-step explanation:
That is the difference between them
if a number became 2.5 times smaller, what precent was it decreased by
Answer:
25 percent because when you change it in percent it came25 percent
Find the missing dimensions: Use the scale factor 1/4:3
Answer:
The answer is 1/4!
Step-by-step explanation:
please help mee!! For which value of x does f(x) = 2?
A) 2
B) 0
C) -4
D) None of the above.
Answer:
The slope is zero
Step-by-step explanation:
0 | 2
1 | 2
3 | 2
Viviana sells handmade necklaces for $12.50 and bracelets for $10.50. On Tuesday,
she sold 24 pieces of jewelry and made $288. How many of each type of jewelry did
she sell?
x= Necklaces
y= Bracelets
Answer:
brainlest = answer
Step-by-step explanation:
Increase 1000 in the ratio 2:5
Answer:
1400
Step-by-step explanation:
2/5×1000=400
1000+400=1400
Step-by-step explanation:
Let the new quantity be x.
x:1000=2:5
x/1000=2/5
(multiply both side by 1000)
[tex]1000 \times \frac{x}{1000} = 1000 \times \frac{2}{5} [/tex]
[tex]x = 400[/tex]
Amanda is 15 years old. She has two sisters, Britney, who is 12 years old, and Caitlin, who is the youngest. Amanda’s age is equal to 3 times the difference of Britney’s age and Caitlin’s age. How old is Caitlin? A. 3 years old B. 5 years old C. 7 years old D. 12 years old
Answer:
c. 7
Step-by-step explanation:
Amanda is 15. 15 is 3 times the age difference so you know the age difference is 5. Britney is 12 so subtract 5 and thats 7.
Answer:
C. 7 Years Old
Step-by-step explanation:
Did the quiz and got 100%
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = 5x - 2
Step-by-step explanation:
y = mx+b
Answer:
y = -5x-2
Step-by-step explanation:
Use slope and y intercept to place the equation into slope intercept for (y=mx+b)
Do number 5 this is not a quiz
Answer:
x = 50 in.
Step-by-step explanation:
72 in. ÷ 36 in. = 2
2 x 25 in.
= 50 in.
A series whose first two terms are -12 to -8 respectively and whose last term is 124
Answer:
first two terms are 6 and 3
Step-by-step explanation:
yuh <3
I got B+ in math what do you think should i tell my parents
Answer:
bro i got a B+ in math tooo!!!!!!!!
Step-by-step explanation:
yeah tell them!
Answer:
It's a low A and your working on bringing it up
Step-by-step explanation:
6.3(1 + f) =
6.3(1 + f) =
Answer:
63 times (f+1)/ 10
Step-by-step explanation:
* Simplify 63 over 10
* 63 over 10 times (f+1)
= 63 times (f+1) over 10
Which set of ordered pairs represents a function?
A. {(0,5), (2,5),(4,5), (6,5), (8,5)}
B. {(3, 1), (3, 2), (3, 3), (3, 4), (3,5)}
C. {(2,3), (3, 4), (4,3), (3, 2), (2, 1)}
D. {(1, 4), (2, 4), (3, 4), (4, 3), (4, 2)}
PLEASE HELP ME OUT
I WILL GIVE BRAINLIEST
PERFORM THE FOLLOWING CONVERSIONS USING UNIT FACTORING
400mg = _____kg
30 cm = _____ mm
f(x) = 3.2 +5 +6
g(x) = 7
Find (f + g)(x).
A. (f+g)(x) = |3x+11| +7
B. (f+g)(x) = |3x+18|
C. (f+g)(x) = |3x+5| + 13
D. (f+g)(x) = |3x| +18
Answer:
A
Step-by-step explanation:
f (x)=3x+5+6
g (x)=7
(f+g)(x)=|3x+5+6|+7
=|3x+11|+7
Is -5/2 greater than 3?
Answer:
No -5/2 is not greater than three.
Step-by-step explanation:
You could solve this without doing any math. You know that a negative divided by a positive is still a negative and that negative numbers are never greater than positive numbers so therefore you got the answer. No, -5/2 is not greater than positive 3.
Answer:
No
Step-by-step explanation:
[tex]-\frac{5}{2}[/tex] is not greater than 3; it is less than 3. Positives are greater than negatives. To know if an integer is negative, you should see something like this: - in front of the number.
Positive integers don't have a plus sign in front of it because we already assume it is there.
Read the scenario. 1. The temperature at 6 A.M. was -5°F. By noon the temperature had risen by 5°F. What was the temperature at noon? Represent these values with integers and model them on a number line. + + + 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 Read the scenario. 2. A diver was 8 feet below sea level. The diver swam back up 8 feet. What is the location of the diver? Represent these values with integers and model them using integer tiles.
Answer:
mm
Step-by-step explanation:
In each figure, solve for X
Answer:
x=15
Step-by-step explanation:
7x+3x-4=146
10x-4=146
10x=150
X=15
The two sides added up equals the outside length.
Hope this helps if this does please mark as brainliest
I don't know what im doing help
Answer:
81/256
Step-by-step explanation:
3/4*3/4*3/4*3/4
first multiply the numerators (3) together, which equals 81
then multiply the denominators (4) together, which equals 256
81/256 can't be simplified further
Answer:
[tex]\frac{3^4}{4^4} =\frac{81}{256}[/tex]
Reasoning:
According to exponent law:
[tex](\frac{a}{b} )^{x} =(\frac{a^x}{b^x} )[/tex]
Now apply this to your problem.
[tex](\frac{3}{4} )^{4}[/tex]
[tex](\frac{3^4}{4^4} )[/tex]
[tex](\frac{81}{256} )[/tex]
2.) Functions or Not a Function? Explain?
Answer:
answer
Step-by-step explanation:
Not a function.
When x repeats, it is automatically not a function. If y repeats, it is still a function.