Question

which statements are true about exponential functions? choose three correct answers.
the range always includes negative numbers.
the graph has a horizontal asymptote at ( x = 0 ).
the input to an exponential function is the exponent.
the base represents the multiplicative rate of change.
the domain is all real numbers.

Explanation:

1. For exponential functions of the form $f(x)=b^x$ where $b>0, b

eq1$:

• The domain is all real numbers, as any real number can be used as the exponent.
• The input (the independent variable $x$) is indeed the exponent in the standard form.
• The base $b$ is related to the multiplicative rate of change: for growth/decay, the rate is tied to $b$ (e.g., $b=1+r$ for growth rate $r$).

1. Incorrect statements:

• The range is all positive real numbers, so it does not include negative numbers.
• The horizontal asymptote is at $y=0$, not $x=0$.

Answer:

• The base represents the multiplicative rate of change.
• The domain is all real numbers.
• The input to an exponential function is the exponent.