Answer:
Option D (fourth choice), a shift right 5 pi/4 units
Step-by-step explanation:
j (x) = 51 cosine (x + StartFraction pi Over 2 EndFraction) + 24
k (x) = 51 cosine (x minus StartFraction 3 pi Over 4 EndFraction) + 24
The answer is the fourth option.
The Required transformation of function j(x) to function k(x) is a shift left StartFraction pi Over 4 EndFraction units.
[tex]j(x)=51\cos(x+\frac{1}{2}\pi)+24\\k(x)=51\cos(x\ -\ \frac{3}{4}\pi)+24[/tex]
Transformation of equation is defined as the change brought to it by adding some difference.
j (x) = 51 cosine (x + StartFraction pi Over 2 EndFraction) + 24
k (x) = 51 cosine (x minus StartFraction 3 pi Over 4 EndFraction) + 24
Though, clearly seen from above equation that the difference between the cos function of both the equation is
1/2pie-3/4pie=90-135
= -45
= - pie/4
The negative sign shows that the curve of k(x) shifts toward -x axis by -pie/4.
Thus, the Required transformation of function j(x) to function k(x) is a shift left StartFraction pi Over 4 EndFraction units.
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