Exponential functions always have restrictions on the range. True or False?

Question

I need to know if there is any exponential function that doesn’t have a restriction on the range, using basic Algebra 2 or Pre-Calculus knowledge.

Answer 1

The x-axis serves as a horizontal asymptote for all exponential functions.  Exponential functions are of the form f(x) = a^x . The domain consists of all real numbers.  However, the range only consists of all numbers greater than zero.  This is because no matter how large x gets, the graph will shoot upwards towards infinity.  If x becomes a negative, we know that we will get f(x) = 1/a² .  The larger the negative number, the closer the function approaches zero.  So, for exponential functions we will always have that restriction that the range will only include positive numbers.  I hope this answers your question. I believe the statement is true.