Question

Review the given functions. j (x) = 51 cosine (x + StartFraction pi Over 2 EndFraction) + 24 k (x) = 51 cosine (x minus StartFraction 3 pi Over 4 EndFraction) + 24 What is the transformation of function j(x) to function k(x)? a shift left StartFraction pi Over 4 EndFraction units a shift left StartFraction 5 pi over 4 EndFraction units a shift right StartFraction pi Over 4 EndFraction units a shift right StartFraction 5 pi over 4 EndFraction units

Answer 1

Answer:

j(x) is shifted right by $\frac{5\pi}{4}$ units

Step-by-step explanation:

Given

$j(x)= 51 cos(x + \frac{\pi}{2})$

$k(x)= 51 cos(x - \frac{3\pi}{4})$

Required

Determine the transformation from j(x) to k(x)

The transformation shows a horizontal shift from j(x) to k(x).

First, we need to determine the unit shifter from j(x) to k(x) as follows;

$j(x)= 51 cos(x + \frac{\pi}{2})$

Express $\frac{\pi}{2}$ as $\frac{5\pi}{4}-\frac{3\pi}{4}$

So:

$j(x)= 51 cos(x + \frac{\pi}{2})$ becomes

$j(x) = 51cos(x + \frac{5\pi}{4}-\frac{3\pi}{4})$

Reorder

$j(x) = 51cos(x -\frac{3\pi}{4}+ \frac{5\pi}{4})$

Comparing this to k(x), we have:

$k(x)= 51 cos(x - \frac{3\pi}{4})$

In other words:

$k(x) = j(x - \frac{5\pi}{4})$

This implies that j(x) is shifted right by $\frac{5\pi}{4}$ units

Answer 2

Answer:

its D

Step-by-step explanation:

a shift right 5 π/4 units