sketch the graph of the function. state the domain and the range, and determine whether the function is…

sketch the graph of the function. state the domain and the range, and determine whether the function is increasing or decreasing.\nf(x)=6^x\nuse the graphing tool to graph the function.\nthe domain of the function is (-∞,∞).\n(type your answer in interval notation.)\nthe range of the function is (0,∞).\n(type your answer in interval notation.)\nis the function increasing or decreasing? select the correct choice below, and, if necessary, fill in the answer box(es) to complete your answer.\n(type your answer in interval notation.)\na. decreasing on\nb. increasing on\nc. increasing on and decreasing on

sketch the graph of the function. state the domain and the range, and determine whether the function is increasing or decreasing.\nf(x)=6^x\nuse the graphing tool to graph the function.\nthe domain of the function is (-∞,∞).\n(type your answer in interval notation.)\nthe range of the function is (0,∞).\n(type your answer in interval notation.)\nis the function increasing or decreasing? select the correct choice below, and, if necessary, fill in the answer box(es) to complete your answer.\n(type your answer in interval notation.)\na. decreasing on\nb. increasing on\nc. increasing on and decreasing on

Answer

Explanation:

Step1: Analyze the function (y = a^x) form

For an exponential function (y=a^x) ((a>0,a\neq1)), when (a > 1), as in (y = 6^x) ((a = 6>1)), the function has certain properties.

Step2: Determine the increasing - decreasing nature

The derivative of (y = 6^x) is (y^\prime=6^x\ln6). Since (6^x>0) for all (x\in R) and (\ln6>0) (because (e\approx2.718<6)), then (y^\prime = 6^x\ln6>0) for all (x\in(-\infty,\infty)).

Answer:

B. Increasing on ((-\infty,\infty))