Question

This is the graph of y = sin(x). Does anyone know the second part?

Answer 1

Answer:

The resulting graph is $y = 5\cdot \sin x$.

Step-by-step explanation:

The resulting function is of the form:

$y = A\cdot \sin x + k$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$A$ - Amplitude, dimensionless.

$k$ - Midpoint value, dimensionless.

The sine function is bounded, between -1 and 1, and must be multiplied by a stretch factor. That is: $A > 0$. According to the graph, the function is bounded between 5 ($y_{max}$) and -5 ($y_{min}$), and the midpoint value ($k$) is 0. The amplitude is determined by the following calculation:

$A = \frac{y_{max}-y_{min}}{2}$

If $y_{min} = -5$ and $y_{max} = 5$, then:

$A = 5$

The resulting graph is $y = 5\cdot \sin x$.

Answer 2

Answers for whole assignment:

(starting after this question)

2) graph 2

3) Minimum: -4

Maximum: 4

Amplitude: 4

zeros: 2nd and 3rd option

4) 2nd graph

5) range of y = sin(x)?

1st one

range of y = 3sin(x)?

2nd one

range of y = –3sin(x)?

2nd one  

range of y = –3sin(x) – 2?

3rd one

6) graph 1

7) graph 3

8) amplitude = 2

midline y = 4

3rd option

9) 2nd option

10) The graph of y = –2sin(x) – 1 is the graph of the parent function stretched vertically by a factor of 2, reflected over the x-axis, and shifted 1 unit down.  The maximum of the parent function is 1, the minimum is –1, and the amplitude is 1.  The maximum of y = –2sin(x) – 1  is 1, the minimum is –3, and the amplitude is 2.