Question

What effect does changing the function f (x) = 2 sin (x/2)- 1 to the function g(x) = 2 sin (x) - 5 have on the graph of f(x)?

O The graph is stretched vertically by a factor of 2 and shifted right 4 units.
O The graph is compressed vertically by a factor of 2 and shifted left 4 units
O The graph is stretched horizontally by a factor of 2 and shifted up 4 units.
O The graph is compressed horizontally by a factor of 2 and shifted down 4 units

Answer 1

choice 4 (or D)

Explanation:

1) the initial argument (x/2) and the final one (x) shows horizontal compression of the given function;

2) the different between (-1) and (-5) is (-4); it means shifting down 4 units;

3) the correct answer is: the graph is compressed horizontally by a factor 2 and shifted down 4 units.

Answer 2

The graph is stretched vertically by a factor of 2 and shifted right 4 units. Option A is correct.

How to transform a function.

Given

f(x) = 2sin(x/2) -1 and g(x) = 2sinx -5

f(x) - 1 = g(x) - 5

f(x) - 1 + 5 = g(x)

f(x) + 4 = g(x)

The graph will shift vertically downward by 4 units

Amplitude Change:

f(x) = 2sin(x/2)

g(x) = 2sin(x)

The coefficients of the sine term remain the same. That is 2. The amplitude of the sine function is doubled (vertically stretched by a factor of 2).

The phase change

sin(x/2) = sin(x)

This means that the peaks and troughs of the graph of g(x) will be twice as high as those of f(x).

Therefore,the graph is stretched vertically by a factor of 2 and shifted right 4 units.