I need help on this question, I can't seem to understand piecewise functions!! ITS SO HARD.
Answers
Answer:
[tex]f(x)\left \{ {{3x+1 if x\leq 0} \atop {-3x+1 if x>0}} \right.[/tex]
Step-by-step explanation:
So if we first graph the given equation, we'll see the graph I've attached below.
Remember that piecewise functions are functions that change based on the circumstances. I know that sounds super confusing, but it's actually really simple!
In this case, for example, we see the line increasing from -∞ to [tex]0[/tex], and then suddenly going downwards and decreasing. That's a good spot for us to notice because that indicates a change. We notice that the function looks different when [tex]x<0[/tex] or [tex]x>0[/tex]. If you break the function into those two parts, you see that they are just linear equations, but they're only visible when x is either greater than or less than 0.
Now that we notice this pattern, we can find the equation of the lines for both lines.
The points (-3,-8) and (-1,-2) are points on the first line, the one that increases (on the left). We can use those points to find the slope of the first line. Remember the slope equation:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Plug in your points:
[tex]m=\frac{-2-(-8)}{-1-(-3)}[/tex]
[tex]m=\frac{6}{2}[/tex]
[tex]m=3[/tex]
So, the slope of the first line is 3. The y-intercept, looking at the graph, is 1. The equation of the first line is [tex]y=3x+1[/tex]. We'll need this later.
Let's do the same thing for the second line. Just looking at the graph, we can see that this is the same exact line, just with a negative slope. So, the equation for the second line is [tex]y=-3x+1[/tex].
So now we can set up a piecewise function.
[tex]f(x)\left \{ {{3x+1} \atop {-3x+1}} \right.[/tex]
The two functions in the bracket are the two different functions used in this graph. Now we need to figure out where each function is effective. Well, they share a y-intercept. Remember that a true function cannot have two points with the same x value. So the first function is effective to the left of x=0, while the second is effective to the right of x=0. In other words, when [tex]x\leq 0[/tex], [tex]f(x)=3x+1[/tex]. But, when [tex]x>0[/tex], [tex]f(x)=-3x+1[/tex]. Now our piecewise function looks like this:
[tex]f(x)\left \{ {{3x+1 if x\leq 0} \atop {-3x+1 if x>0}} \right.[/tex]
And that is our piecewise function for the original function.
I know this is confusing, so please let me know if you have any questions! I hope this helps!
Related Questions
algebra nation section 3- topic 8
Answers
Answer:
POINTSSSS thxx:))
Step-by-step explanation:
In a survey of 2,500 people who owned a certain trote of car, 500 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answers
Answer:
20 %
Step-by-step explanation:
I did the math and its 20
What does 15% + 14% + 12% =
Answers
Answer:
41%
Step-by-step explanation:
adding percentages is just regular adding so 15 + 14 + 12 = 41
Answer:
0.41
Hope this helped you
9. f(x) = x2 - 49, g(x) = x + 7
Answers
Answer:
(x^(2)-49)/(x-7)
Step-by-step explanation:
Did it.
The diagram shows four graphs match the graphs to the equations
Answers
Answer:
y=x^2 is graph D
y=1/x is graph A
otherwise, you're right
Mr Morales makes a table of the number of chaperones needed for different numbers of students attending a field trip. The ratio of parent chaperones to students is a constant proportion. What is the missing number in Mr. Morale’s table?
A) 36
B) 40
C) 42
D) 48
Answers
Answer:
48
Step-by-step explanation:
2 x 8 = 16
4 x 8 = 32
8 x 8 = 64
6 x 8 = 48
2 div 16 = 8
4 div 32 = 8
8 div 64 = 8
6 div 48 = 8
Matthew mixes 1/2 cup of yellow paint for every 1/5 cup of blue paint to make green paint. how many cups of yellow paint are needed for 1 cup of blue paint.
Answers
Answer: He needs 2 1/2 cups of yellow paint
The points (-9, -10) and (-2,-5) form a proportional relationship. Find the slope of the
line that passes through these two points.
Answers
Answer:
[tex]m=\frac{5}{7}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-9, -10)
Point (-2, -5)
Step 2: Find slope m
Substitute: [tex]m=\frac{-5+10}{-2+9}[/tex]Add: [tex]m=\frac{5}{7}[/tex]And we have our final answer!
Divide 25 1858.
To find the quotient, start by dividing
Answers
Answer:
74.32
Step-by-step explanation:
1,858 divided by 25= 74.32
To evaluate any piecewise function you must look at the domain. true or false ?
Answers
To evaluatetheany piecewise function we must look at the domain. Yes it is true.
Put it in your own words
Answers
There's a seasonal show called the Amazing Race. I am chosen to participate in it, my partner is Fransteria. I am the leader of our team. In this game, we have to chose the best path, we have to calculate the fastest way to victory. A map full of triangles will be given to us for the first path. We will get to know about more details later.
Write an equation that represents each graph.
Answers
Answer:
3x3
Step-by-step explanation:
I think that it is 3x3 because that is the angle.
9514 1404 393
Answer:
y = -x +3y = x -3y = 3x +1y = -3x -3Step-by-step explanation:
In each case, the slope can be found by counting the number of vertical grid squares for each horizontal grid square between points where the line crosses grid intersections. The ratio "rise"/"run" is the slope of the line, m.
The y-intercept, b, can be found as the y-value where the line crosses the y-axis.
These values go into the slope-intercept form of the equation for a line to give the equation you want:
y = mx + b
__
1. Rise is -1 for a run of 1. The y-axis is crossed at 3.
y = -x +3
__
2. Rise is 1 for a run of 1. The y-axis is crossed at -3.
y = x -3
__
3. Rise is 3 for a run of 1. The y-axis is crossed at 1.
y = 3x +1
__
4. Rise is -3 for a run of 1. The y-axis is crossed at -3.
y = -3x -3
Question 2
Only students who receive financial aid from the college/university they attend is entitled to take a tax credit.
True
False
Answers
But, I’m not sure. Sorry¯\_(ツ)_/¯
If m2A = 110 degrees and m2B = 35 degrees, find m21.
A)
35 degrees
B)
75 degrees
C)
110 degrees
D)
145 degrees
Answers
Answer:
c
Step-by-step explanation:
i have a degree in mathematics so you can trust this
please answer I need the answer now, please
Answers
Answer:
The slope is -2, and the y-intercept is 12.
Step-by-step explanation:
At 4:00 A.M., the outside temperature was –28°F. By 4:00 P.M. that same day, it rose 38 degrees. What was the temperature at 4:00 P.M.?
Answers
Answer:
10°
Step-by-step explanation:
-28 + 38 = 10
if jogging burns on average 140 calories every 15 minutes. how many calories are you burning in one hour.
Answers
do 60 divided by 15 then do 140 multiplied by what ever you got when you did 60 divided by 15
Jamie plays a trivia game. She earns 1 point for each
correct answer and loses 0.25 points for each incorrect
answer. She gets 15 correct answers and 5 incorrect
answers
What is her score for the game?
A 16.25
B 13.75
C. 15
D. 14.25
Answers
Answer: B. 13.75
First write out the equation you need to solve
1x - 0.25y = total score
Second fill in the known information
1(15) - 0.25(5) = total score
Now solve your equation
15 - 1.25 = total score
13.75 = total score
Her score for the game will be 13.75. Then the correct option is B.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Jamie plays a trivia game.
She earns 1 point for each correct (W) answer and loses 0.25 points for each incorrect (L) answer.
Then the total points is given as
Total point = W – 0.25L
She gets 15 correct answers and 5 incorrect answers.
Then her score for the game will be
Total point = 15 – 0.25 x 5
Total point = 13.75
Then the correct option is B.
More about the linear system link is given below.
https://brainly.com/question/20379472
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how do I solve this
Answers
Answer:
15 degrees
Step-by-step explanation:
7x - 15 = 90
+15. +15
7x = 105
divide both sides by 7
x = 105/7 = 15
Your class collected money to buy turkeys and hams for
the local food shelter. After the collection, your class
had exactly enough money to buy 11 hams and 9
turkeys. If you raised a total of $316, and each turkey
cost $18, how much is one ham?
Answers
Answer: $14.00
Step-by-step explanation:
9 turkeys costed a total amount of $162.00
We need to subtract that from the total cost, $316.00, to find out how much money was spent on 11 hams.
316 - 162 = 154
So, 11 hams costed 154.
We then need to find the unit rate of 11 turkeys for 154 dollars.
To do that, we must divide 154 ÷ 11
That gives us 14.
Therefore, your answer is: $14.00 per ham.
Jahaira buys a car for $5,160. Her state charges 7% sales tax, $87
for licence plates, and $30 for safety and emissions fees. How much
will Jahaira owe for these extra charges, NOT INCLUDING the price
of the car?
Answers
Answer:
119.1
Step-by-step explanation:
I’m not good at Spanish but,
Yo esta una decepción
Can Spanish people translate to the ones who don’t understand?
Answers
Answer:
Yo esta una decepcion? Alright, a direct translation would be: I this a deception/disappointment, but for it to make sense it would be either I'm disappointed, or I'm disappointed of her, due to "esta" is to refer a women non dearingly
Step-by-step explanation:
I am a disappointment.
Yo esta = I am
una = a
decepción = disappointment
También puedo suponer que ya soy una decepción para usted.
This can be translated to:
I can also imagine that I'm already a disappointment to you.
Ms. Shepheard cuts 1/2 of a piece of a construction paper. She uses 1/6 of the piece to make a flower. What fraction of the sheet of paper dose she use to make the flower.
Answers
Answer:
She use 1/12 of the paper
Step-by-step explanation:
please answer see the image below
Answers
Answer:
64.8Step-by-step explanation:
total area = rectangle + semi circle
= (11 x 5) + (1/2 * π * 2.5²)
= 55 + 9.8
= 64.8 sq. units
Answer:
64.8² units. Hope it's help you.
Triangle JKL is reflected across x = 0 and then translated 5 units up to create △JʹKʹLʹ. Are the two figures congruent? Explain.
A. No; a reflection changes the orientation of a figure, so the figures are not congruent.
B. No; a translation changes the position of a figure, so the figures are not congruent.
C. Yes; reflections and translations preserve lengths and angle measures, so the figures are congruent.
D. There is not enough information.
Answers
Answer:C
Step-by-step explanation: Measure stay the same when translated
The solution is Option C.
Yes; reflections and translations preserve lengths and angle measures, so the figures are congruent
What are Congruent Triangles?
Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the triangle be represented as Triangle ΔJKL
Now , the triangle JKL is reflected across the line x = 0
So , the triangle is reflected along the y axis
And , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
So , the x coordinates of triangle JKL changes
Now , the triangle is translated 5 units up
So , the values of the y coordinates gets increased by 5 units
And the transformed triangle is ΔJ'K'L'
The transformed triangles retains the shape as well the angle measures
From the congruent theorem of triangles
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
So , the triangle ΔJKL ≅ ΔJ'K'L'
Hence , the triangles are congruent and reflections or translations preserve lengths and angle measures
To learn more about congruent triangles click :
https://brainly.com/question/26131452
#SPJ1
Probability of rolling a composite number on a dice and the coin landing on tails
Answer choices are 1/8, 2/3 and 5/6
This is 7th grade math btw
Answers
Answer:
5/6.
Step-by-step explanation:
The only composite numbers on a die are 4 and 6, so the probability of landing on them is 2/6 or 1/3. The probability of landing on tails on a coin is 1/2. Add them together (1/3 + 1/2) and you get the total probability of 5/6.
I hope this helps.
slope of y = 7x-100
Answers
Answer:
The slope equals 7.
Step-by-step explanation:
Following the formula y = mx + b where:
m = slope
x = independent variable
b = y-intercept
our equation looks like:
y= 7x - 100
m = 7
x = x
b = -100
If slope = m and m = 7 then we can conclude that the slope = 7.
Is 8397 divisible by 9
Answers
Answer: yes
Step-by-step explanation:
If the sum of the digits is not divisible by 9, then 8397 is not divisible by 9. 27 is divisible by 9, Therefore, 8397 is divisible by 9 and the answer to the question, "Is 8397 Divisible By 9?" is Yes.
Answer:
Yes
Step-by-step explanation:
PLease see the picture below please help me thank you.
Answers
3r +8
combine 4r -r
combine 14 -6
3r + 8
Math assignment cant get it
Answers
Answer:
y = -1/2x + (-1)
Step-by-step explanation:
