Answer:
The range of y is [tex][-\dfrac{5}{2},\dfrac{1}{2}][/tex]
Step-by-step explanation:
Given: [tex]y=\dfrac{3}{2}\cos (4x) -1[/tex]
It is cosine function of trigonometry.
We need to find the range of given function. The value of y shows range of function.
y is depends on cosine function.
As we know cosine max/min value is fixed.
y is max when cosine max.
y is min when cosine is min.
Maximum value of cosine = 1
[tex]y_{max}=\dfrac{3}{2}(1) -1=\dfrac{1}{2}[/tex]
Minimum value of cosine = -1
[tex]y_{min}=\dfrac{3}{2}(-1) -1=-\dfrac{5}{2}[/tex]
Range of y: [min,max]
Range: [tex][-\dfrac{5}{2},\dfrac{1}{2}][/tex]
Hence, The range of y is [tex][-\dfrac{5}{2},\dfrac{1}{2}][/tex]
