which statements are true about exponential functions? check all that apply. the domain is all real numbers…

Explanation:

Step1: Analyze domain

An exponential function is of the form $y = a\cdot b^{x}$, where $x$ can be any real - number. So the domain is all real numbers.

Step2: Analyze range

For $y = a\cdot b^{x}$, if $a>0$ and $b > 0$, $y>0$. If $a < 0$ and $b>0$, $y<0$. But in general, the range does not always include negative numbers. For example, $y = 2^{x}$, the range is $y>0$.

Step3: Analyze horizontal asymptote

The graph of an exponential function $y = a\cdot b^{x}+k$ has a horizontal asymptote at $y = k$. For $y = a\cdot b^{x}$ (where $k = 0$), the horizontal asymptote is at $y = 0$, not $x = 0$.

Step4: Analyze input

In an exponential function $y = a\cdot b^{x}$, the input is $x$ (the independent variable), not the exponent. The exponent is the power to which the base is raised.

Step5: Analyze base

In an exponential function $y=a\cdot b^{x}$, the base $b$ represents the multiplicative rate of change. If $b>1$, the function is increasing, and if $0 < b<1$, the function is decreasing.

Answer:

The domain is all real numbers. The base represents the multiplicative rate of change.