Even function:
A function is said to be even if its graph is symmetric with respect to the , that is:
Odd function:
A function is said to be odd if its graph is symmetric with respect to the origin, that is:
So let's analyze each question for each type of functions using examples of polynomial functions. Thus:
FOR EVEN FUNCTIONS:
1. When becomes
1.1 Effects on the y-intercept
We need to find out the effects on the y-intercept when shifting the function into:
We know that the graph intersects the y-axis when , therefore:
So:
So the y-intercept of is one unit less than the y-intercept of
1.2. Effects on the regions where the graph is increasing and decreasing
Given that you are shifting the graph downward on the y-axis, there is no any effect on the intervals of the domain. The function increases and decreases in the same intervals of
1.3 The end behavior when the following changes are made.
The function is shifted one unit downward, so each point of has the same x-coordinate but the output is one unit less than the output of . Thus, each point will be sketched as:
FOR ODD FUNCTIONS:
2. When becomes
2.1 Effects on the y-intercept
In this case happens the same as in the previous case. The new y-intercept is one unit less. So the graph is shifted one unit downward again.
An example is shown in Figure 1. The graph in blue is the function:
and the function in red is:
So you can see that:
2.2. Effects on the regions where the graph is increasing and decreasing
The effects are the same just as in the previous case. So the new function increases and decreases in the same intervals of
In Figure 1 you can see that both functions increase at:
and decrease at:
2.3 The end behavior when the following changes are made.
It happens the same, the output is one unit less than the output of . So, you can write the points just as they were written before.
So you can realize this concept by taking a point with the same x-coordinate of both graphs in Figure 1.
FOR EVEN FUNCTIONS:
3. When becomes
3.1 Effects on the y-intercept
We need to find out the effects on the y-intercept when shifting the function into:
As we know, the graph intersects the y-axis when , therefore:
And:
So the new y-intercept is the negative of the previous intercept shifted one unit upward.
3.2. Effects on the regions where the graph is increasing and decreasing
In the intervals when the function increases, the function decreases. On the other hand, in the intervals when the function decreases, the function increases.
3.3 The end behavior when the following changes are made.
Each point of the function has the same x-coordinate just as the function and the y-coordinate is the negative of the previous coordinate shifted one unit upward, that is:
FOR ODD FUNCTIONS:
4. When becomes
4.1 Effects on the y-intercept
In this case happens the same as in the previous case. The new y-intercept is the negative of the previous intercept shifted one unit upward.
4.2. Effects on the regions where the graph is increasing and decreasing
In this case it happens the same. So in the intervals when the function increases, the function decreases. On the other hand, in the intervals when the function decreases, the function increases.
4.3 The end behavior when the following changes are made.
Similarly, each point of the function has the same x-coordinate just as the function and the y-coordinate is the negative of the previous coordinate shifted one unit upward.
Can someone please help me out Its really Important please marking brainliest
Answer:
Q1. Volume of the prism
= 75(20)(14) cm3
=21000 cm3
Volume of the cylinder
= π(75^2)(120)cm3
=2120575cm3 (cor. to nearest int.)
The cylindrical bale has a greater volume.
Q3a. Volume of the pyramid
=(1/3)(40)(64)(64)m3
=54613 m3 (cor. to nearest int.)
Q3b. Volume of air per person
=(1/3)(40)(64)(64)(1/5000) m3
=10.9 m3 (cor to 3 sig fig)
Solve the equation |8y+4|=2|y−1|.
Explain.
[tex]\\ \sf\longmapsto |8y+4|=2|y-1|[/tex]
[tex]\\ \sf\longmapsto 8y+4=2y-1[/tex]
[tex]\\ \sf\longmapsto 8y-2y=-1-4[/tex]
[tex]\\ \sf\longmapsto 6y=-5[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{-5}{6}[/tex]
Johnny has 304 apples, his sister ate 301 of them. How many apples does he have? After His sister ate the apples a magic fairy multiplied the apples by 281893.21 times. Now how many apples does Johnny have. After the faity multiplied the apples a demon can and divided the apples by pi * the square root of 9284. Now how many apples does Johnny have?
Answer:
1. John still has 3 Apples
2. John now has 845679,63 Apples (I'm not sure if you've written the number of the multiplying fairy right...).
3. If the * is multiplying:
John now has 25937228,2 Apples.
Step-by-step explanation:
Just use the calculator.
DONT UNDERSTAND THE QUESTION CAN SOMEONE HELP ME!!!
Answer:
246.62007 cm. HTH!
Step-by-step explanation:
A=2AB+(a+b+c)h
AB=s(s﹣a)(s﹣b)(s﹣c)
s=a+b+c
2
Solving forA
A=ah+bh+ch+1
2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=8·9+5·9+10·9+1
2·﹣84+2·(8·5)2+2·(8·10)2﹣54+2·(5·10)2﹣104≈246.62007
Answer ASAP please!
………
Answer:
47.746, answer choice C
Step-by-step explanation:
47.746
if the ordered pairs (x-2,3y+1) and (y+1,x+3) are equal,find x and y
plz help me
factor and solve problem in picture pleaseeee
I hope it's right have a great day :)
Simplify the expression
Answer:
B
Step-by-step explanation:
[tex] \frac{{3}^{5} }{ {3}^{3} } = {3}^{5 - 3} = {3}^{2} = 9 [/tex]
HELP ME ASAP!!!
two angles are supplementary. one angle is three less than 4 times it's supplement. what are the measures of the two angles?
Step-by-step explanation:
Two angles are supplementary one angle is 4 degrees less than three times the other find the measures of the angles
x + y = 180
x = 3y - 4
3y - 4 + y = 180
4y = 184
y = 46
x = 134
Answer:
30°,150°
Step-by-step explanation:
Given the following coordinates complete the glide reflection transformation.
hopefully this answer can help you to answer the next question.
If the triangle on the grid below is translated three units left and nine units down, what are the coordinates of C"?
your outlook on the increasing spread of epidmics
Answer:
increasing spread epidemics your outlook
The difference between interior angle in centesimal measurement and sexagesimal measurement is 15° of a regular polygon. Find the number of sides of the polygon.
Answer:
8
Step-by-step explanation:
x = centesimal angle (100 degrees in a right angle)
y = sexagesimal angle (90 degrees in a right angle)
x - y = 15
x×90/100 = y
x×9/10 = y
x - x×9/10 = 15
10x/10 - 9x/10 = 15
x/10 = 15
x = 150
y = 150×9/10 = 15×9 = 135
using centesimal system :
the sum of all external angles in a polygon is 400 degrees (a full circle).
one external angle is the complement of one internal angle to 200 degrees = 200-150=50 degrees.
to find the number of sides of the polygon we need to find the number of angles or corners. and that is how many external angles fit into the full circle.
n = 400/50 = 8
the polygon has 8 sides
3. Find the product, using suitable properties :
a) 26 x (-48) + (-48) x (-36)
b) 625 x (-35) + (-625) x 65
please answer fast 10 marks
a) 26 x (-48) + (-48) x (-36) = ( –1248) + ( + 1728) = – 1248+ 1728 = 480
b) 625 x (-35) + (-625) x 65 = ( –21875) + ( –40625) = – 21875 –40625 = –62500
I hope I helped you^_^
which expression is equivalent to 2^5/6^5
Answer:
Step-by-step explanation:
I can't give you either B or D, but I can calculate the answer.
2^5
=====
(2^5)(3^5)
The 2^5s cancel out.
1
===
3^5
Another answer could be 3^-5
or
0.004115
Bob is hired by Company A and is given an annual salary of $35 000 with a 10% raise
after 1 year. Sam is hired by Company B and is paid $3842.42 per month with a 5% raise
after 1 year. Determine the difference of salary after 1 year.
Step-by-step explanation:
Bob's salary : $35000 per year plus 10% after one year
100% = 35000
1% = 100%/100 = 35000/100 = $350
10% = 10×1% = 10×350 = $3500
so in total, his salary will be $35000+$3500 = $38500 after one year.
Sam's salary : $3842.42 per month plus 5% after one year.
100% = $3842.42 per month. but to make it comparable to Bob's salary, we need to calculate the annual salary.
so, 100% 12×3842.42 = $46109.04
1% = 100%/100 = 46109.04/100 = $461.09
5% = 5×1% = 5×461.09 = $2305.45
so, in total, his salary will be $46109.04+$2305.45 = $
Divide. Write your answer in simplest form.
−0.18÷0.03=
HI THERE
the answer is -6
#YoghurtCup
hlol can u plz solve b no plz plz.....I will mark as brainliest
Answer:
Step-by-step explanation:
[tex]Tan \ B =\frac{4}{3} = \frac{opposite \ side \ of B}{adjacent \ side \ of B}[/tex]
BC = 15 cm
3x = 15
x = 15/3 = 5
AB =4x = 4*5 = 20 cm
Pythagorean theorem,
AC² = AB² + BC²
= 20² + 15 ²
= 400 + 225
= 625
AC = √625 = 25 cm
AC = 25 cm
[tex]Sin \ A = \frac{opposite \ side \ of \ angle A }{hypotenuse}\\\\ = \frac{BC}{AB}=\frac{15}{25}=\frac{3}{5}[/tex]
What’s the coordinates for Y-3>2x+2 on a graph?
someone help me with this
find points a b c
Answer:
<a=32
<b=40
<c=40
Step-by-step explanation:
to find angle a you have to subtract the 50 minus 180 to find the angle close to the 50 because angles in a straight line add up to 180. the answer will be
180-50=130
after finding the angle in that triangle you must add it to the other angle present which is 18° then subtract by 180 because angles in a straight line add up to 180
130+18+a=180
a=180-148
a=32 and that's how you find a
to find b you must know that the angle at the center is twice the angle at the circumference meaning the large angle C is 90°,now if it's 90° inorder to find the big angle B you must add the 18+90 then subtract 180
18+90+B=180
B=180-108
=72
since the combination of angle a and b will give you 72 you can find angle c by subtracting a from 72
c=72-32
=40
then if you look at angle c and angle b you can tell that they are alternating meaning angle b is also 40
I hope this helps
What does 2x+1=3x-4 equal?
Answer:
5
Step-by-step explanation:
2x + 1 = 3x - 4
-2x -2x
--------------------
1 = x - 4
+4 +4
----------------
5 = x
The answer is 5.
Hope this helped.
quadratics formula 4x^2+3x-1=0
Answer: X = 1/4 or X = -1
Step-by-step explanation:
4x2+3x−1=0
(4x−1)(x+1)=0
4x−1=0 or x+1=0
4x=1 or x=-1
Now divide 4 from both sides
like this 4x/4=1/4
now cancel out two 4's so the answer will be x=1/4
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
A sample of 1000 U.S. pediatricians is taken to collect data on medicines used to treat children. The population in this study is ___________________.
A. all U.S. pediatricians
B. the children who are taking medicine
C. the medicine used to treat children
D. the 1000 pediatricians
Answer:
the awnser is d 1000 pediatricians
Solve for x.
A) - 9
C) -5
B) -11
D) 10
Answer: D) 10
Step-by-step explanation:
All angles in a triangle adds up to 180°
60° + 50° + 7x = 180°
7x = 180° - 60° - 50° = 180°- 110° = 70°
x = (70 ÷ 7)° = 10°
find the common ratio 3, 9, 27, 81
What equation represents the parabola with focus (-1,4) and directrix y= -2
Answer:
Hello
y=(x+1)/12 +1
Step-by-step explanation:
[tex]\text{As the directrice is horizontal:}\\\\\\y=-2 ==> k=-2\\\\Focus=(a,b)=(-1,4)\\\\\boxed{y=\dfrac{x-a}{2(b-k)} +\dfrac{b+k}{2} }\\\\\\y=\dfrac{x+1}{2(4+2)} +\dfrac{4-2}{2} }\\\\\boxed{y=\dfrac{x+1}{12} +1}\\[/tex]
7t + 6 + 3v + 6v
Hey can someone help ne
Answer:
7t + 6 + 9v
Step-by-step explanation:
7t + 6 + 3v + 6v (since 3v and 6v are like terms you will add them both.)
7t + 6 + 9v
Hope this helps, thank you :) !!
Answer:
7t+6+9v
Step-by-step explanation:
7t+6+3v+6v
7t has no opponent it is =7t
6 is on it own =6
3v+6v=9v,reason is 3v has an opponent which is 6v so addition of 3v and 6v is =9v
so ur ans. is =7t+6+9v
what expressions are equivalent to 5+(-3)(6x-5)
Answer:
Hi!
Step-by-step explanation:
-5 (x-3) + 3(4 - x) + 2x
Let's distribute the -5 within its parentheses.
A negative multiplied by a negative number has a positive result.
Let's distribute the 3 within its parentheses.
-5x+15+12-3x+2x
Combine like terms...
-5x-3x+2x=-6x
15+12=27
-6x+27
Both numbers are divisible by 3...
3(-2x+9)
or -3...
-3(2x-9)
Violet is playing a board game with her friends. She earns 78 points during the game, and she receives a game-end bonus for achieving her secret objective. With her bonus, Violet came in second place with 91 points. Let b be the number of points Violet earned for the game-end bonus. Write and solve an equation for b.
Answer:
13
Step-by-step explanation:
78 + b = 91 Equation: Subtract 78 from both sides.
b = 91 - 78
b = 13
You don't need her position in the game or the fact that 91 placed her second.
HELP! I'LL GIVE BRAINLIEST ! ! ! ! ! ! ! !
Select all of the quadrants that the parabola whose equation is y = √x - 4 (principal square root) occupies.
a. IV b. III c. II d. I
Quadrants I and IV
When we graph y^2 = x - 4, we see that it is on the x axis, and goes up into Quadrant I, and down into Quadrant IV