## Exponential functions

Our textbook defines an exponential function as
f(x) = ab^x. However, a question was brought up about a function, g(x) = 5^sqrt(x). Is g an exponential function? It looks like an exponential graph for x>0, but is not continuous on R.

 PhysOrg.com mathematics news on PhysOrg.com >> Pendulum swings back on 350-year-old mathematical mystery>> Bayesian statistics theorem holds its own - but use with caution>> Math technique de-clutters cancer-cell data, revealing tumor evolution, treatment leads
 Blog Entries: 9 Recognitions: Homework Help Science Advisor A function is not defined in the absence of domain and range. So do tell us the whole definition as worded by your book.

 Quote by drewfstr314 Our textbook defines an exponential function as f(x) = ab^x. However, a question was brought up about a function, g(x) = 5^sqrt(x). Is g an exponential function? It looks like an exponential graph for x>0, but is not continuous on R.
Let us ignore the fact that g(x) = 5^sqrt(x) is not always real-valued for negative x and ask the somewhat better defined question:

"Does the graph of g(x) = 5^sqrt(x) match the graph of any function f(x) of the form ab^x for real-valued constants a and b and positive real x"

One simple-minded way to answer this would be to assume that there is such a function and realize that, if so:

f(0) = a*b^0 = a = g(0) = 5^sqrt(0) = 1

So a = 1

f(1) = a*b^1 = ab = b = g(1) = 5^sqrt(1) = 5

So b = 5

So the question then becomes:

"does the graph of g(x) = 5^sqrt(x) match the graph of f(x) = 5^x"

The answer to that question is rather obvious.

 Similar discussions for: Exponential functions Thread Forum Replies Precalculus Mathematics Homework 9 Precalculus Mathematics Homework 4 Precalculus Mathematics Homework 14 Calculus & Beyond Homework 4