begin by graphing ( f(x)=log x ). use transformations of this graph to graph the given function. graph and…

begin by graphing ( f(x)=log x ). use transformations of this graph to graph the given function. graph and give the equation of the asymptote. use the graphs to determine the functions domain and range.\n( h(x)=log x - 2 )\ngraph ( h(x)=log x - 2 ). graph the asymptote of ( h(x) ) as a dashed line. use the graphing tool to graph the function.

begin by graphing ( f(x)=log x ). use transformations of this graph to graph the given function. graph and give the equation of the asymptote. use the graphs to determine the functions domain and range.\n( h(x)=log x - 2 )\ngraph ( h(x)=log x - 2 ). graph the asymptote of ( h(x) ) as a dashed line. use the graphing tool to graph the function.

Answer

Explanation:

Step1: Identify parent function

Parent function: $f(x) = \log x$ (base 10 implied). Its asymptote is $x=0$, domain is $(0,+\infty)$, range is $\mathbb{R}$.

Step2: Determine transformation

$h(x) = \log x - 2$ is $f(x)$ shifted down 2 units. Vertical shifts don't change asymptote, domain, or range.

Step3: Find asymptote of h(x)

Asymptote remains $x=0$ (vertical asymptote for log functions).

Step4: Domain of h(x)

Logarithm input must be positive: $x > 0$, so domain is $(0,+\infty)$.

Step5: Range of h(x)

Vertical shift doesn't restrict output; range is all real numbers, $\mathbb{R}$.

Answer:

Asymptote equation: $x=0$
Domain: $(0, +\infty)$
Range: $(-\infty, +\infty)$

(Note: Graphing requires plotting $h(x)$ as $f(x)$ shifted down 2 units, with dashed line $x=0$.)