Question

What effect does changing the function f(x)=3sin(x)+1to the function g(x)=3sin(x/4)+2 have on the graph of f(x)?




The graph is compressed vertically by a factor of 4 and shifted right 1 unit.

The graph is stretched horizontally by a factor of 4 and shifted up 1 unit.

The graph is stretched vertically by a factor of 4 and shifted down 1 unit.

The graph is compressed horizontally by a factor of 4 and shifted left 1 unit.

Answer 1

Answer:

The graph is stretched horizontally by a factor of 4 and shifted up 1 unit

Step-by-step explanation:

Answer 2

The effect of transforming the function is (b) The graph is stretched horizontally by a factor of 4 and shifted up 1 unit

How to interpret the transformations of the functions?

The functions are given as:

f(x) = 3sin(x)+1

g(x) = 3sin(x/4)+2

Start by stretching the function f(x) horizontally by a scale factor of 4.

So, we have:

f'(x) = 3sin(x/4) + 1

Next, shift the function f'(x) upward by 1 unit.

So, we have:

f'(x) = 3sin(x/4) + 1 + 1

Evaluate the sum

f'(x) = 3sin(x/4) + 2

Rewrite as:

g(x) = 3sin(x/4) + 2

Hence, the effect of transforming the function is (b) The graph is stretched horizontally by a factor of 4 and shifted up 1 unit

Read more about function transformation at:

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