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Regarding the properties of some functions, analyze the following statements: a) Determine the exponent of the following functions: b) Analyze the ...
Regarding the properties of some functions, analyze the following statements:
a) Determine the exponent of the following functions:
b) Analyze the properties of the following functions:
c) Analyze the injectivity of the following functions:
d) Analyze the monotonicity of the following functions:
e) Determine which functions admit inverse:
a) ????(????) has an even exponent, since ????(????) ≥ 0 for all ???? in its domain.
b) ????(????) = ???????? has a positive exponent, since it is defined for ∀ ???? ∈ ℝ. If the exponent were negative, the function would not be defined for ???? = 0.
b) ????(????) = ???????? has a null exponent, since ????(????) = 1 = ????0.
b) ℎ(????) = ???????? has a positive exponent, since it is defined for ∀ ???? ∈ ℝ. If the exponent were negative, the function would not be defined for ???? = 0.
b) ????(????) = ???????? has a negative exponent, since the function is not defined for ???? = 0.
b) ℎ(????) = ???????? has a positive exponent, since it is defined for ∀ ???? ∈ ℝ. If the exponent were negative, the function would not be defined for ???? = 0.
b) ????(????) = ???????? has a positive exponent, since it is defined for ∀ ???? ∈ ℝ. If the exponent were negative, the function would not be defined for ???? = 0.
b) ????(????) = ???????? has a negative exponent, since the function is not defined for ???? = 0.
c) The functions ????(????) = ????????, ????(????) = ????????, ????(????) = ???????? are injective, since their graphs meet the 'Horizontal Line Test'.
c) The functions ℎ(????) = ????????, ????(????) = ????????, ????(????) = ???????? are not injective, since their graphs are not 'approved' in the 'Horizontal Line Test'.
d) ????(????) = ???????? is always increasing.
d) ????(????) = ???????? is constant, ????(????) = 1, ∀ ???? ∈ ℝ.
d) ℎ(????) = ???????? is decreasing in the interval (−∞, 0] and is increasing in the interval [0, +∞).
d) ????(????) = ???????? is decreasing in the intervals (−∞, 0) and (0, +∞).
d) ????(????) = ???????? is always increasing.
d) ????(????) = ???????? is increasing in the interval (−∞, 0) and is decreasing in the interval (0, +∞).
e) The functions that admit inverse are: ????(????) = ????????, ????(????) = ????????, ????(????) = ????????. Note that the graphs of these functions are 'approved' in the 'Horizontal Line Test'.
a) All statements are correct.
b) All statements are correct.
c) All statements are correct.
d) All statements are correct.
e) All statements are correct.
a) Determine the exponent of the following functions:
b) Analyze the properties of the following functions:
c) Analyze the injectivity of the following functions:
d) Analyze the monotonicity of the following functions:
e) Determine which functions admit inverse:
a) ????(????) has an even exponent, since ????(????) ≥ 0 for all ???? in its domain.
b) ????(????) = ???????? has a positive exponent, since it is defined for ∀ ???? ∈ ℝ. If the exponent were negative, the function would not be defined for ???? = 0.
b) ????(????) = ???????? has a null exponent, since ????(????) = 1 = ????0.
b) ℎ(????) = ???????? has a positive exponent, since it is defined for ∀ ???? ∈ ℝ. If the exponent were negative, the function would not be defined for ???? = 0.
b) ????(????) = ???????? has a negative exponent, since the function is not defined for ???? = 0.
b) ℎ(????) = ???????? has a positive exponent, since it is defined for ∀ ???? ∈ ℝ. If the exponent were negative, the function would not be defined for ???? = 0.
b) ????(????) = ???????? has a positive exponent, since it is defined for ∀ ???? ∈ ℝ. If the exponent were negative, the function would not be defined for ???? = 0.
b) ????(????) = ???????? has a negative exponent, since the function is not defined for ???? = 0.
c) The functions ????(????) = ????????, ????(????) = ????????, ????(????) = ???????? are injective, since their graphs meet the 'Horizontal Line Test'.
c) The functions ℎ(????) = ????????, ????(????) = ????????, ????(????) = ???????? are not injective, since their graphs are not 'approved' in the 'Horizontal Line Test'.
d) ????(????) = ???????? is always increasing.
d) ????(????) = ???????? is constant, ????(????) = 1, ∀ ???? ∈ ℝ.
d) ℎ(????) = ???????? is decreasing in the interval (−∞, 0] and is increasing in the interval [0, +∞).
d) ????(????) = ???????? is decreasing in the intervals (−∞, 0) and (0, +∞).
d) ????(????) = ???????? is always increasing.
d) ????(????) = ???????? is increasing in the interval (−∞, 0) and is decreasing in the interval (0, +∞).
e) The functions that admit inverse are: ????(????) = ????????, ????(????) = ????????, ????(????) = ????????. Note that the graphs of these functions are 'approved' in the 'Horizontal Line Test'.
a) All statements are correct.
b) All statements are correct.
c) All statements are correct.
d) All statements are correct.
e) All statements are correct.
