f(x)=10^{x} and g(x)=log(x). select all the statements that are true.\na the graph of f(x)=10^{x} has a…

f(x)=10^{x} and g(x)=log(x). select all the statements that are true.\na the graph of f(x)=10^{x} has a horizontal asymptote.\nb the range of f(x) is the same as the domain of g(x).\nc the graph of g(x)+log 100 is a translation of up 2 of the graph of g(x).\nd one of the functions is always increasing, and one of them is always decreasing.\ne the graph of g(x)=log x has a vertical asymptote.

f(x)=10^{x} and g(x)=log(x). select all the statements that are true.\na the graph of f(x)=10^{x} has a horizontal asymptote.\nb the range of f(x) is the same as the domain of g(x).\nc the graph of g(x)+log 100 is a translation of up 2 of the graph of g(x).\nd one of the functions is always increasing, and one of them is always decreasing.\ne the graph of g(x)=log x has a vertical asymptote.

Answer

Explanation:

Step1: Analizar la función ( f(x) = 10^{x} )

La función ( y = a^{x}) ((a>1)) tiene una asíntota horizontal (y = 0). Entonces ( f(x)=10^{x}) tiene una asíntota horizontal (y = 0). Además, el rango de ( f(x)=10^{x}) es ( (0,\infty)).

Step2: Analizar la función ( g(x)=\log(x))

La función ( y=\log(x)) tiene dominio ( (0,\infty)) y una asíntota vertical (x = 0).

Step3: Analizar (g(x)+\log(100))

Como ( \log(100)=\log(10^{2}) = 2), entonces (g(x)+\log(100)=\log(x)+2). Según la regla de traslación (y = f(x)+k) (traslación vertical (k) unidades), para (k = 2) es una traslación hacia arriba de 2 unidades de (y=\log(x)).

Step4: Analizar el crecimiento de las funciones

La función ( y = 10^{x}) es creciente ya que la base (a = 10>1) y la función (y=\log(x)) es creciente ya que la base (a = 10>1) (ya que (y=\log_{a}(x)) con (a>1) es creciente).

Answer:

A. The graph of (f(x)=10^{x}) has a horizontal asymptote. B. The range of (f(x)) is the same as the domain of (g(x)). C. The graph of (g(x)+\log(100)) is a translation of up 2 of the graph of (g(x)). E. The graph of (g(x)=\log(x)) has a vertical asymptote.