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3 years ago

What’s is the domain of f(x) ?

Mathematics

1 answer:

marusya05 [52]3 years ago

4 0

Answer:

Step-by-step explanation:

The inputs are -1, 0, 1 and 2. This set represents the domain of the function.

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Workers on the assembly line produce 4x + 6 boats each day. Which expression shows how many boats they produced in 12 days?

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We're going to assume that x = # of days.
Plug 12 in as x:
4 × 12 = 48
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3 years ago

Explain the rule in solving inequalities with a negative coefficient.

dimulka [17.4K]

Answer:

the comparison must be reversed when multiplying by a negative

Step-by-step explanation:

The rules of equality apply to solving inequalities, with the exception that multiplication or division by a negative number reverses the sense of the comparison:

-x > 1

x < -1 . . . . . multiply both sides by -1

____

Effectively, multiplication (or division) by a negative number is equivalent to reflection across the origin. Things that were ordered left/right (on the number line) are ordered right/left after such a reflection:

-2 < -1

1 < 2

_____

<em>Additional comment</em>

Application of any function requires that you pay attention to ordering. Some functions naturally reverse the order; others do so only on specific domains.

Consider f(x) = 1/x.

1 < 2

f(1) > f(2) . . . . because the slope of the f(x) function is negative everywhere.

<em>In the first and second quadrants</em>, the cosine function also reverses order.

20° > 10°

cos(20°) < cos(10°)

Probably the most commonly encountered function used with inequalities is the absolute value function.

|x-3| > 2

This function has one domain where the slope is negative, and another domain where the slope is positive.

For x < 3, the function negates its argument, so we have ...

-(x -3) > 2

-x +3 > 2

-x > -1

x < 1 . . . . . everywhere consistent with x < 3

For x ≥ 3, the function does nothing, so we have ...

x -3 > 2

x > 5

The solution to this absolute value inequality is (x < 1) ∪ (x > 5).

You can also resolve negative coefficients by adding the opposite. Addition and subtraction never require any change to the comparison operator.

-x > 1

0 > x +1 . . . . x is added

-1 > x . . . . . . -1 is added

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3 years ago

Beth says that the graph of g(x) = + 1 is a translation of 5 units to the left and 1 unit up of f(x) = . She continues to explai

Nata [24]

Beth's description of the transformation is incorrect

<h3>Complete question</h3>

Beth says that the graph of g(x)=x-5+1 is a translation of 5 units to the left and 1 unit up of f(x) = x. She continues to explain that the point (0,0) on the square root function would be translated to the point (-5,1) on the graph of g(x). Is Beth's description of the transformation correct? Explain

<h3>How to determine the true statement?</h3>

The functions are given as:

g(x) = x - 5 + 1

f(x) = x

When the function f(x) is translated 5 units left, we have:

f(x + 5) = x + 5

When the above function is translated 1 unit up, we have:

f(x + 5) + 1 = x + 5 + 1

This means that the actual equation of g(x) should be

g(x) = x + 5 + 1

And not g(x) = x - 5 + 1

By comparison;