Which of the functions have a range of all real numbers? Check all that apply.
2 answers:
<h2>Hello!</h2>
The answer is: The correct options are B. Tan(x) and C. Cot(x)
<h2>Why?</h2>The range is the output of a function when we evaluate the function with inputs (domain), not all functions have a range of all real numbers, however it's more common to find functions without range or domain restrictions.
Both options B. Tan(x) and C. Cot(x) have a range of all real numbers while the functions Sec(x) and Csc (x) have a restricted range.
Sec(x) and Csc(x):
Domain, all real numbers.
Range, from -1 to 1 or [-1,1]
Tan(x) and Cot(x):
Domain, all real numbers except
Range, all real numbers.
Hence, the correct options are B. Tan(x) and C. Cot(x)
Have a nice day!
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Answer:
The following Triangles are Right Triangles:
1. Δ ABC Where AB = 76 in, BC = 357 in, and AC = 365 in.
2. Δ MIT Where MI = 123 cm, IT = 836 cm, and MT = 845 cm.
3. Δ MEL Where ME = 20 ft, EL = 99 ft, and ML = 101 ft.
Step-by-step explanation:
For a Triangle to be a Right Triangle it must Satisfy Pythagoras theorem.
i.e.
For Δ ABC Where AB = 76 in, BC = 357 in, and AC = 365 in.
AC² = 365² = 133225
AB² + BC² = 76² + 357² = 1333225
∴ AC² = AB² + BC²
Hence Δ ABC a Right Triangle.
For Δ MIT Where MI = 123 cm, IT = 836 cm, and MT = 845 cm.
MT² = 845² = 71405
MI² + IT² = 123² + 836² = 714025
∴ MT² = MI² + IT²
Hence Δ MIT a Right Triangle.
For Δ MEL Where ME = 20 ft, EL = 99 ft, and ML = 101 ft.
ML² = 101² = 10201
ME² + EL² = 20² + 99² = 10201
∴ ML² = ME² + EL²
Hence Δ MEL a Right Triangle.