the domain of an exponential function is all real numbers. the range of an exponential function is positive…
the domain of an exponential function is all real numbers. the range of an exponential function is positive real numbers. complete the graph of an exponential function has a y - intercept only. complete the graph is decreasing throughout its domain and has at the x - axis because the value close to 0 but never reach it. a slope line an asymptote a tangent line
Answer
Explanation:
Step1: Recall exponential - function properties
For an exponential function (y = b^{x}(b>1)), the domain is all real numbers because we can substitute any real - number value for (x).
Step2: Analyze the range
Since (b>1), for any real number (x), (b^{x}>0). So the range is positive real numbers.
Step3: Find the intercept
When (x = 0), (y=b^{0}=1). So the graph has a (y) - intercept at ((0,1)) and no (x) - intercept (because (b^{x}\neq0) for all real (x)).
Step4: Determine the behavior and asymptote
The function (y = b^{x}(b > 1)) is increasing throughout its domain. As (x\to-\infty), (y = b^{x}\to0). The (x) - axis ((y = 0)) is an asymptote because the function values get closer and closer to 0 but never reach it.
Answer:
The domain of an exponential function is all real numbers. The range of an exponential function is positive real numbers. The graph of an exponential function has a y - intercept only. The graph is increasing throughout its domain and has an asymptote at the x - axis because the values get close to 0 but never reach it.