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

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1. In the function f(x), x is replaced with 2x 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 represents time in hours since the beginning of the 24-hour period, that models the situation?

Feb 18, 2018

#1
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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

Feb 18, 2018