Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x). How did the transformation affect the domain and range of the function?
You can use tables, graphs, or equations to justify your answer.
Answers
The two graphs are represented below.
Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.
There are 3 ways to change a function:
Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;Now, the points for f(x) are:
(-5,0) (0,6) (5,-4) (8,0)
And the points for g(x) are:
(-5,-3) (0,-9) (5,1) (8,-3)
Comparing points:
(-5,0) → (-5,-3)
(0,6) → (0,-9)
(5,-4) → (5,1)
(8,0) → (8,-3)
It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:
(-5,0-3) → (-5,-3)
(0,6-15) → (0,-9)
(5,-4+5) → (5,1)
(8,0-3) → (8,-3)
Then, the vertical change is a Vertical Shift.
Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.
Range of a function is all the values y can assume after substituting the x-values.
Domain of a function is all the values x can assume.
Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.
Any vertical translation will change the range of a function and keep domain intact.
Then, for f(x) and g(x):
graph translation domain range
f(x) none [-5,8] [-4,6]
g(x) vertical shift [-5,8] [-9,1]
In conclusion, this transformation (or translation) will affect the range of g(x)
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Answers
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Step-by-step explanation:
And usually means to add, so combine your like terms:
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x^5 + x^2 = x^7
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Answer:
Step-by-step explanation:
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= 84x⁷y¹⁶
In exponents multiplication, if base are same, then add the powers.
xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾
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Answer:
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Step-by-step explanation:
Answer on plato
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Answer:
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Step-by-step explanation:
Find the factors.
36
Find the factors.
48
Find the quotient.
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Find the quotient.
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Answer:
Step-by-step explanation:
36
=
48
=
0.5334
=
0.06
=
75.1
=
10
=
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hey...
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Answer:2
Step-by-step explanation:
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If the function f(x) = 4x + 2 and g(x) = (5/2)x - 4.
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More about the function link is given below.
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heir ht eit theeir t erehr ther eht ere there there hterh there jt there htererh there ht ereh the the the the the the thetthe they they they they they tyh ththbey they theyetheir theitr te there ther there the there htere h
Step-by-step explanation:
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The amount of milk left after making the pancakes is 52 fluid ounces.
What is a Ratio?A ratio indicates the number of times one number contains another.
Given that, Stacy has 2 quarts of milk.
Since there are 32 fluid ounces in one quart, it follows:
1 quart = 32 fluid ounces
2 quart = 64 fluid ounces
Therefore, Stacy has 64 fluid ounces of milk.
Now, she used 12 fluid ounces of milk in making pancakes, therefore, the amount of milk left after making the pancakes is:
64 - 12
= 52
Hence, the amount of milk left after making the pancakes is 52 fluid ounces.
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Josie's Bagel Shop recently sold 3 poppy seed bagels and 3 other bagels. What is the experimental probability that the next bagel sold will be a poppy seed bagel? Simplify your answer and write it as a fraction or whole number, P(poppy seed bagel) Submit
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Answer:
ffbhjdhjdfahdsfsdfakfawlefgwaheghfgawlygfailwegfalawegfuwlgweilfygweiyaglifwafawegwegerg
Step-by-step explanation:
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If the measure of <1 = 112 what is the measure of <6?
112
100
68
180
Answers
Answer:it’s 68
Step-by-step explanation:
I think
Answer:
m∠6=68°
Step-by-step explanation:
∠1 and ∠2 are supplementary angles, which means they add up to 180°
180-112=68
∠2 and ∠6 are corresponding angles, so they are the same
m∠6=68°
