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Dibuje la gráfica de la función logarítmica
f(x)=log_(2)(x+4) e indique lo siguiente:

El dominio de la función.
La asíntota vertical.
Los interceptos con los ejes (si los hay).

Dibuje la gráfica de la función logarítmica $f(x)=\log _{2}(x+4)$ e indique lo siguiente: $\newline$ - El dominio de la función. $\newline$ - La asíntota vertical. $\newline$ - Los interceptos con los ejes (si los hay).

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Quotient property of logarithms

Full solution

Q. Dibuje la gráfica de la función logarítmica

f(x)=\log _{2}(x+4)

e indique lo siguiente:

\newline

- El dominio de la función.

\newline

- La asíntota vertical.

\newline

- Los interceptos con los ejes (si los hay).

Find Domain: Find the domain of the function. $\newline$ Reasoning: The argument of the logarithm must be greater than $0$ . $\newline$ Calculation: x + 4 > 0 $\newline$ x > -4 $\newline$ Domain: $(-4, \infty)$
Vertical Asymptote: Identify the vertical asymptote. $\newline$ Reasoning: The vertical asymptote occurs where the argument of the logarithm is $0$ . $\newline$ Calculation: $x + 4 = 0$ $\newline$ $x = -4$ $\newline$ Vertical Asymptote: $x = -4$
Find x-intercept: Find the x-intercept. $\newline$ Reasoning: The x-intercept occurs where $f(x) = 0$ . $\newline$ Calculation: $\log_2(x + 4) = 0$ $\newline$ $x + 4 = 2^0$ $\newline$ $x + 4 = 1$ $\newline$ $x = -3$ $\newline$ x-intercept: $(-3, 0)$
Find y-intercept: Find the y-intercept. $\newline$ Reasoning: The y-intercept occurs where $x = 0$ . $\newline$ Calculation: $f(0) = \log_2(0 + 4)$ $\newline$ $f(0) = \log_2(4)$ $\newline$ $f(0) = 2$ $\newline$ y-intercept: $(0, 2)$

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