Match each verbal description to its equivalent function rule as applied to the given function below. 3a – 7 = 6 - 9 = -3.1 14 (1) و = 3x - 7 = 121 – 19 = 60 - 2 = -31 28 The function fstretched vertically by a factor of 4 and translated up by 9 units The function ftranslated 6 units up and 2 units right The function freflected about the y-axis and translated 7 units left The function f stretched vertically by a factor of 2 and translated up by 5 units
Answers
Answer:f(x) = 3x - 7
6 up; 2 right = 3(x-2) - 7 + 6
= 3x - 6 - 7 + 6
= 3x - 7
reflected about y-axis; 7 left = -3(x+7) -7
= -3x - 21 - 7
= -3x - 28
up 5 ; 2 vert stretch = (2)(3x - 7) + 5
= 6x - 14 + 5
= 6x - 9
up 9 ; 4 vert stretch = (4)(3x - 7) + 9
= 12x - 28 + 9
= 12x - 19
Step-by-step explanation:
The transformation of a function may involve any change. The function f(x) stretched vertically by a factor of 2 and translated up by 5 units is (6x - 9).
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift:
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)Given the function f(x)=3x-7, which can be transformed as shown below.
1. The function f(x) stretched vertically by a factor of 4 and translated up by 9 units.
Vertical stretch → 4(3x - 7) = 12x - 28
Up by 9 Units → (12x - 28) + 9
g(x) = 12x - 19
2. The function f(x) translated 6 units up and 2 units right
Up by 6 units → (3x - 7) +6 = 3x - 1
2 units Right → 3(x-2) - 1 = 3x - 6 - 1 = 3x - 7
g(x) = 3x - 7
3. The function f(x) reflected about the y-axis and translated 7 units left
Reflected about the y-axis → -3x - 7
7 units left → -3(x+7) - 7 = -3x - 21 -7 = -3x-28
g(x) = -3x-28
4. The function f(x) stretched vertically by a factor of 2 and translated up by 5 units
Stretched vertically by a factor of 2 → 2(3x - 7) = 6x - 14
Translated up by 5 units → 6x - 14 + 5 = 6x - 9
g(x) = 6x - 9
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Related Questions
What is the inverse of the function g(x) = x + 16?
Answers
Answer:
[tex]g {}^{ - 1} (x) = 2 \sqrt[3]{x - 16} [/tex]
choose (2)
Jordan is baking brownies and chooses to use a round pan. The diameter of the pan is 12 inches. What is the area of the pan? Round to the nearest tenth.
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Which of the following is an arithmetic sequence?
Answers
Arithmetic sequences are defined by a common difference between the numbers that’s both constant and consecutive.
To break it down:
The first option is {-1, 3, -3, -1}, which appears to be alternating, and there is more than 1 difference between the n term values. That is:
-1 to 3 = increase of 4
3 to -3 = decrease of 6
-3 to -1 = increase of 2
Therefore does not follow the definition of an arithmetic sequence.
The second option (the answer) {2, -2, -6, -10} is arithmetic, as it consistently and thus consecutively decreases by 4.
Finally, the last two sequences have the same issue with their pattern, {3, 6, 9, 15}
and {4, 14, 24, 32}. In which they stay constant for the first three n terms, but suddenly change in value on the 4th n term. Therefore, they are not arithmetic.
I hope this helped!
WILL GIVE BRAINIEST
Keith writes the numbers 1 to 20 on pieces of paper and places them in a hat. The probability of randomly selecting a number less than 16 is . Choose the likelihood that best describes the probability of this event. A. Neither likely nor unlikely B. Impossible O C. Likely D. Unlikely
Answers
Answer: Likely
Step-by-step explanation: I got it right!
Answer:
C. Likely
Step-by-step explanation:
Hope it helps :)
Amanda bought 2 CDs that were each the same price. Including sales tax, she paid a total of $29.80. Each CD had a tax of $1.10 . What was the price of each CD before tax?
brainliest
Answers
Answer:
13.80 there you go buddy
Find the volume and show work (round to the tenths)
Answers
Answer:
120 km^3
Step-by-step explanation:
the base is a right triangle
A = (leg1 x leg2)/2 = (6 x 8)/2 = 24 km^2
the volume of a prism is base area x height
V = 24 x 5 = 120 km^3
Answer:
2000
Step-by-step explanation:
Find the cosine of 300°. Round your answer to the nearest hundredth, if necessary.
-0.87
-0.5
0.5
0.87
Answers
Answer:
option C . 0.5
Step-by-step explanation:
[tex]cos 300 = cos(2\pi - 300 ) = cos( 360 - 300) = cos 60 = 0.5[/tex]
Using the formula :
[tex]cos\theta = cos (2\pi - \theta )[/tex]
C= 0.5
Step-by-step explanation:
how do I make a box plot
Answers
Answer:
To construct a box plot, use a horizontal or vertical number line and a rectangular box. The smallest and largest data values label the endpoints of the axis. The first quartile marks one end of the box and the third quartile marks the other end of the box
Answer:
this may help
Step-by-step explanation:
A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value. We use these values to compare how close other data values are to them. To construct a box plot, use a horizontal or vertical number line and a rectangular box.
Solve the expression for a=12 b=6 and c=3
Answers
Answer:
36
Step-by-step explanation:
I did the work on my notebook
Answer:
Step-by-step explanation:
c(a+b)-bc
=3(12+6)-6*3
=36+18-18(plus 18 and minus 18 gets cancel)
=36
Josh says that −5/4 has the same quotient as 5/−4 . Is this true or false?
Answers
Answer:
true 100%
Step-by-step explanation:
Here is an inequality: -2x>10
List some values for x that would make this inequality true.
Answers
Answer:
The right solution is "[tex]x>-5[/tex]".
Step-by-step explanation:
The given inequality is:
⇒ [tex]-2x>10[/tex]
By solving the above expression, we get
⇒ [tex]x >-\frac{10}{2}[/tex]
⇒ [tex]x>-5[/tex]
Thus the above is the correct answer.
what is 14.235 rounded to t nearest tenth
Answers
Answer:
14.2
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
THE ANSWER IS 14.2
Step-by-step explanation:
pleasee helppppp im so close to being done and this is my last day !!
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ANSWER FOR UR QUESTION!
Graph
Find f(f(x))
Describe the Transformation
Find the Domain of the Composition f(f(x))
Solve for x
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Solve by Graphing
Multiply. Express your answer in simplest form. 2/3 x 5/6. Show work.
Answers
Step-by-step explanation:
[tex] \frac{2}{3} \times \frac{5}{6} \\ = \frac{10}{18} \\ = \frac{5}{9} [/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
If these two triangular puzzle pieces are to be made congruent, what must be the measure of angle z?
Answers
Answer:
116
Step-by-step explanation:
180-28=152
152-36=116
What is the approximate measure of the length of the tennis court, x? A. 49.9 ft B. 72.0 ft C. 93.1 ft D. 78.0 ft
Answers
Solve graphically: 2x - y = 7 and x - 2y = 5.
Answers
Answer:
(3, - 1)
Step-by-step explanation:
We want to solve the system of equations:
2*x - y = 7
x - 2*y = 5
graphically.
To do it, we need to graph both lines, it will be easier if we rewrite both lines in a more general way, like in the slope-intercept form:
y = -7 + 2*x
y = -(5/2) + x/2
Now, a solution of the system is a point (x, y) such that the point is a solution to both equations, then, when we graph the lines, as that point belongs to both equations, we should see that both lines pass through that point.
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Below, you can see a graph of the lines, and is easy to see that the lines do intersect at the point (3, - 1)
Is the statement true or false?
If x = 6, then x can
only be equal to 6.
True
False
Copyright © 2003 - 2021 Asellus Corporation
Answers
The answer is false
The statement "If |x| = 6, then x can only be equal to 6" is false.
The absolute value of a number represents its distance from zero on the number line.
The expression |x| = 6 means that the distance of x from zero is 6. Therefore, x can be either positive or negative 6.
In this case, x can be either 6 or -6 because both numbers have an absolute value of 6.
Hence, x is not limited to being equal to only 6.
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Would you rather (A) Run for 12 minutes at least 10 miles and hour; ... OR ... (B) 20 minutes at 6 miles per hour?
Answers
PLS HELP ILL MARK AS BRAINLIST AND FOLLOW U
Answers
Answer:
[tex]31\:\text{square units}[/tex]
Step-by-step explanation:
We can break the composite figure into two triangles and two trapezoids. The area of a triangle is given by [tex]A=\frac{1}{2}bh[/tex] and the area of a trapezoid is given by [tex]A=\frac{b_1+b_2}{2}\cdot h[/tex] (average of the bases multiplied by the height).
Area of first triangle (larger triangle to the figure's left): [tex]\frac{1}{2}\cdot 4\cdot 4=8[/tex]
Area of second triangle (smaller triangle to the figure's right ): [tex]\frac{1}{2}\cdot 2\cdot 5=5[/tex]
Area of first trapezoid (smaller trapezoid directly underneath second triangle and adjacent to both triangles): [tex]4\cdot 2 =8[/tex]
Area of first triangle (larger triangle to the figure's left): [tex]5\cdot 2=10[/tex]
Thus, the area of the entire figure is:
[tex]8+5+8+10=\boxed{31\:\mathrm{units^2}}[/tex]
find the volume of the following prism..helpppp pleasee!!!
Answers
Answer:
Step-by-step explanation :The volume V of a prism is V = Bh, where B is the area of the base, h is the height of the prism.To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
Answer:
volume of the prism
(20×12×10)-(8×8×20)
2400-1280
1120 cm³
3. Which of the following is not equal to sin(270°)?
(1) cos(180)
(3) -sin (90)
(2) - cos(0)
(4) sin(360)
Answers
y is inversely proportional to x.
When x=9, y = 8.
Find y when x= 6.
Answers
Answer:
y = 12 when x = 6
Step-by-step explanation:
The equation for inverse proportion is
xy = k where k is a constant
Let x = 9 and y = 8
9*8 = k
72 = k
The equation is xy = 72
Let x=6
6*y = 72
Divide each side by 6
6y/6 = 72/6
y =12
PLEASE HELP
A
B
C
D
???
Answers
find the measure of the angle of elevation of the sun to the nearest degree, if a 100ft tall building casts a 150ft shadow.
Answers
Answer:
33.7º
Step-by-step explanation:
tan = opp/adj
tan∅ = 100/150 = 2/3
∅ = arctan 2/3
∅ = 33.690067525979787
33.7º
Mr. McGregor has plowed a square plot of land to make a garden. The area of the square garden is 256 ft. To the 2nd power
What is the length of one side of the garden?
Answers:
16 ft
32ft
64ft
128ft
Answers
Answer:
16 ft
Step-by-step explanation:
Area = Side^2 = (s)^2 = 256, Side = 16.
So, 16 ft.
Mark this as Brainliest if this was correct! I really appreciate it! :D
Answer:
16ft
Step-by-step explanation:
find the area of a circle with a radius of 5 ft
Answers
Answer:
2.5 feet bud hope it helps
Which of the following sets do NOT represent Equivalent expression?
Answers
Answer:
Only B.
Step-by-step explanation:
Only B because 36/12 does not equal to 12/36!
What's the rule for the following sequence?
4, 1, -2, -5, …
Answers
Answer:
7-3n
Step-by-step explanation:
the difference between 4, 1 is 1 -4= -3
the difference between 1, -2 is-2-1=-3
The formula is a + (n-1)d => 4 + (n-1)-3
=> 4 -3n +3
=> 7-3n
Answer:
Subtract -3
Step-by-step explanation:
4--3 is 1, 1--3 is -2, -2- -3 is -5, when subtracting negatives they add together to from a bigger negative.
Please with explanation
Answers
Answer:
7.5 ,9.1 ans. hhfjvfbhhvvnjgvjki