given that the point (8, 3) lies on the graph of $g(x)=log_2x$, which point lies on the graph of…

given that the point (8, 3) lies on the graph of $g(x)=log_2x$, which point lies on the graph of $f(x)=log_2(x + 3)+2$?\n(5, 1)\n(5, 5)\n(11, 1)\n(11, 5)

given that the point (8, 3) lies on the graph of $g(x)=log_2x$, which point lies on the graph of $f(x)=log_2(x + 3)+2$?\n(5, 1)\n(5, 5)\n(11, 1)\n(11, 5)

Answer

Explanation:

Step1: Analyze transformation of functions

The function $f(x)=\log_2(x + 3)+2$ is a transformation of $g(x)=\log_2x$. The $x+3$ inside the logarithm shifts the graph of $g(x)$ 3 units to the left, and the $+ 2$ outside the logarithm shifts the graph 2 units up.

Step2: Apply transformation to the given point

For the $x$-coordinate of the point on $g(x)$ which is $x = 8$, after the left - shift of 3 units, the new $x$-coordinate is $8-3=5$. For the $y$-coordinate of the point on $g(x)$ which is $y = 3$, after the up - shift of 2 units, the new $y$-coordinate is $3 + 2=5$.

Answer:

$(5,5)$