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

Explanation:

Step1: Analyze domain

For an exponential function of the form $y = a\cdot b^{x}$, $x$ 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, $y = 2^{x}$, $y>0$.

Step3: Analyze horizontal asymptote

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

Step4: Analyze input

The input to an exponential function is the variable in the exponent, but we usually call it the independent variable $x$, not the exponent itself. The exponent is an expression involving the input variable.

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.