Which of the following functions are continuous for all real numbers? g(x)=2^(x) f(x)=ln(x) Choose 1 answer: (A) g only (B) f only (C) Both g and f (D) Neither g nor f

Analyze g(x) = 2^x: Analyze the function g(x) = 2^x. The function g(x) = 2^x is an exponential function with a base greater than 1. Exponential functions are continuous for all real numbers because there are no breaks, jumps, or holes in the graph of an exponential function.Analyze f(x) = ln(x): Analyze the function f(x) = ln(x). The function f(x) = ln(x) is the natural logarithm function. The domain of the natural logarithm function is (0, ∞), which means it is only defined for positive real numbers. Therefore, f(x) is not continuous for all real numbers because it is not defined for x ≤ 0.Determine continuity: Determine which functions are continuous for all real numbers. Based on the analysis, g(x) = 2^x is continuous for all real numbers, while f(x) = ln(x) is not. Therefore, the correct choice is that only g(x) is continuous for all real numbers.

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Which of the following functions are continuous for all real numbers?

g(x)=2^(x)

f(x)=ln(x)
Choose 1 answer:
(A)
g only
(B)
f only
(C) Both
g and
f
(D) Neither
g nor
f

Which of the following functions are continuous for all real numbers? $\newline$ $g(x)=2^{x}$ $\newline$ $f(x)=\ln (x)$ $\newline$ Choose $1$ answer: $\newline$ (A) $g$ only $\newline$ (B) $f$ only $\newline$ (C) Both $g$ and $f$ $\newline$ (D) Neither $g$ nor $f$

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Algebra 1

Domain and range of quadratic functions: equations

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Q. Which of the following functions are continuous for all real numbers?

\newline

g(x)=2^{x}

\newline

f(x)=\ln (x)

\newline

Choose

1

answer:

\newline

(A)

g

only

\newline

(B)

f

only

\newline

g

and

f

\newline

(D) Neither

g

nor

f

Analyze $g(x) = 2^x$ : Analyze the function $g(x) = 2^x$ . The function $g(x) = 2^x$ is an exponential function with a base greater than $1$ . Exponential functions are continuous for all real numbers because there are no breaks, jumps, or holes in the graph of an exponential function.
Analyze $f(x) = \ln(x)$ : Analyze the function $f(x) = \ln(x)$ . The function $f(x) = \ln(x)$ is the natural logarithm function. The domain of the natural logarithm function is $(0, \infty)$ , which means it is only defined for positive real numbers. Therefore, $f(x)$ is not continuous for all real numbers because it is not defined for $x \leq 0$ .
Determine continuity: Determine which functions are continuous for all real numbers. $\newline$ Based on the analysis, $g(x) = 2^x$ is continuous for all real numbers, while $f(x) = \ln(x)$ is not. Therefore, the correct choice is that only $g(x)$ is continuous for all real numbers.