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AURORKA [14]
2 years ago
9

How does the graph of g(x) = (x - 3)^3 - 2 differ from the group of f(x) = x^3?

Mathematics
1 answer:
Vinvika [58]2 years ago
6 0

Answer:

B

Step-by-step explanation:

f(x) = x³

g(x) = (x - 3)³ - 2

The inside of the parenthesis represents a horizontal shift

If the number operation being done to x inside of the parenthesis is adding ( or if the number is positive ) then the graph will shift to the left. If the operation being done inside of the parenthesis to x is subtraction ( or if the number is negative ) then the graph will shift to the right.

The operation being done is subtraction therefore it will shift to the right. So it will go 3 units to the right.

the number on the outside works like a y intercept. if it's positive it goes up, if it's negative it goes down. the number is -2 so it will go down 2 units

we can conclude that g is shifted 3 units right and 2 units down

the answer is B

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Joint variation states that:

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From the given information: The volume V of a gas varies inversely as the pressure P and directly as the temperature

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by definition of joint variation:

V = k\frac{T}{P}  .....[1] where k is the constant of variation.

It is also given that a certain gas has a volume of 10 liters(L) , a temperature of 300 kelvins(K), and a pressure of 1.5 atmosphere(atm).

Substitute these given values in [1] to solve for k;

10 = k\frac{300}{1.5}

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Divide by 200 both sides we have;

k = \frac{10}{200} =\frac{1}{20}

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Now substitute the given data and value of k in [1] we have;

V = \frac{1}{20} \cdot \frac{400}{5} = \frac{20}{5} = 4

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