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zavuch27 [327]
3 years ago
13

How does changing the function from f(x) = 3 sin 2x to g(x) = 3 sin 2x + 5 affect the range of the function?

Mathematics
2 answers:
Margarita [4]3 years ago
8 0

Answer:

Change in function f(x) to g(x): 5 unit up

Range: [2,8]

Step-by-step explanation:

Given:

f(x)=3\sin2x

g(x)=3\sin(2x)+5

First we have to see the change from f(x) to g(x).

g(x)=3\sin(2x)+5

g(x)=f(x)+5

f(x)=3\sin2x

If we shift f(x) 5 unit up to get g(x)

g(x)=3\sin(2x)+5

Effect: f(x) shift 5 unit up

Now we see change in range.

Range of f(x)=3\sin2x

[-3,3]

Graph shift 5 unit up.

So, Range will shift 5 unit up.

Range of g(x)=3\sin(2x)+5

[-3+5,3+5]\Rightarrow [2,8]

Hence, The range of g(x) is [2,6]

Travka [436]3 years ago
4 0
The difference between f(x) and g(x) is the +5 . Adding 5 to the end will increase all y-values obtained for the function. The range is all possible y-values of the function. The function is a wave, which moves between high and low points; +5 in the positive y direction and -5 in the negative y direction is increasing the range by 10.
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Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has
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Answer:

Please find attached the required plot accomplished with an online tool

Part A:

1/4

Part B:

P''(-1, 0),  Q''(0, -1), and R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent

Step-by-step explanation:

Part A:

Triangle ΔPQR has vertices P(4, 0), Q(0, -4), R(-8, -4)

Triangle ΔP'Q'R' has vertices P'(1, 0), Q'(0, -1), R'(-2, -1)

The dimensions of the sides of the triangle are given by the relation;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates on the ends of the segment

For segment PQ, we place (x₁, y₁) = (4, 0) and (x₂, y₂) = (0, -4);

By substitution into the length equation, we get;

The length of segment PQ = 4·√2

The length of segment PR = 4·√10

The length of segment RQ = 8  

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The length of segment P'R' = √10

The length of segment R'Q' = 2

Therefore, the scale factor of the dilation of ΔPQR to ΔP'Q'R' is 1/4

Part B:

Reflection of (x, y) across the y-axis gives;

(x, y) image after reflection across the y-axis = (-x, y)

The coordinates after reflection of P'(1, 0), Q'(0, -1), R'(-2, -1) across the y-axis is given as follows;

P'(1, 0) image after reflection across the y-axis = P''(-1, 0)

Q'(0, -1) image after reflection across the y-axis = Q''(0, -1)

R'(-2, -1) image after reflection across the y-axis = R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent as the dimensions of the sides of triangle PQR and P''Q''R'' are not the same.

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Which expression shows the miles you would drive from the grocery store to the office along this road?
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To increase an amount by 30%, what single multiplier would you use? and To decrease an amount by 30%, what single multiplier wou
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Tina has been dieting for a total of 13 weeks she lost 3 pounds on the first week of her dad but gain back a pound on the second
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So Tina has been dieting for 13 weeks


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On week 2: She gained a pound, so - 1 pound

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