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3 years ago

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]3 years ago

6 0

Answer:

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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4 years ago

Which number line represtents the solution to |x+4|=2?

vlada-n [284]

Answer:

Points -2 and -6 on the number line are the two solutions.

Step-by-step explanation:

Use the definition of absolute value as a starting point

$|x|=x\,\,\mbox{for}\,\,x\geq 0\\|x|=-x\,\,\mbox{for}\,\,x$

To solve the equation, you need to treat the two cases as above:

$|x+4|=x+4=2\,\,\,\mbox{for}\,\,x+4\geq 0\implies x\geq -4\\x+4=2\implies x=-2$

The solution x=-2 is consistent with the condition x>=-4, so it is the first and valid solution. Now the second case of the absolute value:

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Again, the second solution -6 complies with the requirement that x<-4, so it is valid.

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3 years ago

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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