1. In the function f(x), *x* is replaced with 2*x* and 1 is added to the function.

f(x)=−3sinx

What effect does this have on the graph of the function?

Options:

The graph is vertically stretched by a factor of 2 and shifts down 1 unit.

The graph is vertically stretched by a factor of 2 and shifts up 1 unit.

The graph is horizontally compressed by a factor of 2 and shifts down 1 unit.

The graph is horizontally compressed by a factor of 2 and shifts up 1 unit.

2. Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5.15 ft at midnight, rises to a high of 10.2 ft, falls to a low of 0.1 ft, and then rises to 5.15 ft by the next midnight.

What is the equation for the sine function f(x), where *x *represents time in hours since the beginning of the 24-hour period, that models the situation?

Guest Feb 18, 2018

#1**+1 **

First one :

The graph is horizontally compressed by a factor of 2 and shifts up 1 unit.

Here are the graphs : https://www.desmos.com/calculator/umiqrxhmie

Second One

2. Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5.15 ft at midnight, rises to a high of 10.2 ft, falls to a low of 0.1 ft, and then rises to 5.15 ft by the next midnight.

In the form y = Asin (Bx) + C

C = 5.15

The amplitude, A, is [ 10.2 - .1] / 2 = 5.05

And we can find B as

2pi / 24 = pi/ 12

So....the function is y = 5.05sin ((pi/12) x ) + 5.15

Here's the graph : https://www.desmos.com/calculator/7k1p2hksdu

CPhill
Feb 18, 2018