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alex41 [277]
3 years ago
15

Can someone help me with this!!! Will give you all my points and brainliest.

Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
7 0

The function is shifted to the right 3 units

a shift to the right is subtracted inside the function

g(x) = f(x-3)

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19.4mm what the lower bound correct to 1dp
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Answer:

The lower bound of 19.4 is 19.35

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What is 0.2(5x – 0.3) – 0.5(–1.1x + 4.2) simplified? 0.2 [5x + (–0.3)] + (–0.5)(–1.1x + 4.2) x – 2.16
dedylja [7]

0.2(5x – 0.3) – 0.5(–1.1x + 4.2) = 6.5x – 2.06

Solution:

Given expression is 0.2(5x – 0.3) – 0.5(–1.1x + 4.2).

To simplify the expression, first multiply the common term within the bracket.

0.2(5x – 0.3) – 0.5(–1.1x + 4.2)

            = (5x × 0.2 – 0.3 × 0.2)  + (–1.1x × (–0.5) + 4.2 × (–0.5))

            = (1x – 0.06) + (5.5x – 2.1)

            = x – 0.06 + 5.5x – 2

Combine like terms together.

            = x + 5.5x – 0.06 – 2

            = 6.5x – 2.06

0.2(5x – 0.3) – 0.5(–1.1x + 4.2) = 6.5x – 2.06

Hence the simplified form of 0.2(5x – 0.3) – 0.5(–1.1x + 4.2) is 6.5x – 2.06.

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Answers:

  • Domain is (-4, 3]
  • Range is (-5, 5]

=====================================================

Explanation:

The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that -4 < x \le 3. It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).

The interval -4 < x \le 3 then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.

It says: x is between -4 and 3. It can't equal -4 but it can equal 3.

So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.

--------------------------------------------------

The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.

The range as a compound inequality is -5 < y \le 5. This condenses into the shorthand of (-5, 5] which is the range in interval notation.

Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.

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