find the domain of the function and then graph the function on your own. use the graph to identify the…

find the domain of the function and then graph the function on your own. use the graph to identify the asymptotes and intercepts. enter \dne\ if there is no intercept or asymptote.\n$f(x)=4\\log x + 3$\ndomain:\nasymptote:\n$x$-intercept: ( , 0)\n$y$-intercept: (0, )\nquestion help: video ebook written example

find the domain of the function and then graph the function on your own. use the graph to identify the asymptotes and intercepts. enter \dne\ if there is no intercept or asymptote.\n$f(x)=4\\log x + 3$\ndomain:\nasymptote:\n$x$-intercept: ( , 0)\n$y$-intercept: (0, )\nquestion help: video ebook written example

Answer

Explanation:

Step1: Find the domain

For the function (y = \log x), the argument of the logarithm must be positive. For (f(x)=4\log x + 3), we have (x>0). So the domain is ((0,\infty)).

Step2: Find the (y -)intercept

Set (x = 0). But (\log(0)) is undefined. So the (y -)intercept is DNE.

Step3: Find the (x -)intercept

Set (y=0), then (4\log x+3 = 0). First, subtract 3 from both sides: (4\log x=-3). Then divide by 4: (\log x=-\frac{3}{4}). Using the definition (\log x = a\Rightarrow x = 10^{a}), we get (x = 10^{-\frac{3}{4}}=\frac{1}{\sqrt[4]{10^{3}}}=\frac{1}{\sqrt[4]{1000}}\approx0.1778).

Step4: Find the asymptote

The vertical asymptote of (y = \log x) is (x = 0). For (y=4\log x+3), the vertical asymptote remains (x = 0).

Answer:

Domain: ((0,\infty)) (y -)intercept: DNE (x -)intercept: ((10^{-\frac{3}{4}},0)) (or approximately ((0.1778,0))) Asymptote: (x = 0)