Question

The graph of f(x) = sin(x) is transformed to a new function, g(x), by stretching it vertically by a factor of 2 and shifting it 3 units
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What is the equation of the new function g (x)?
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Answer 1

Answer:   g(x) = 2sin(x)+3

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Explanation:

We start with y = sin(x) or f(x) = sin(x). Recall that y = f(x) since both are outputs.

Vertically stretching by a factor of 2 means we multiply each y value by 2.

This means,

y = sin(x)

2y = 2sin(x)

Then we shift 3 units up. So we add 3 to the y coordinate

2y+3 = 2sin(x)+3

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We can track an example point to see this movement in action. For instance, let's focus on the point (pi/6,1/2) which is on f(x). I'm in radian mode.

Stretching f(x) vertically by a factor of 2 means (pi/6,1/2) moves to (pi/6, 1) after the stretching occurs. I multiplied the y coordinate by 2, and kept the x coordinate the same.

Then we shift up 3 units to go from (pi/6, 1) to (pi/6, 4). You add 3 to the y coordinate and keep the x coordinate the same. Note that plugging x = pi/6 into g(x) = 2sin(x)+3 leads to 4.  

Answer 2

Answer:

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

Explanation: