Question

Which one of the following is not correct for the features of exponential function given by $f(x)=b^x$ where $b>1$ ?

• A. The domain of the function is $R$, the set of real numbers.
• B. The range of the function is the set of all positive real numbers
• C. For very large negative values of $x$, the function is very close to $0$.
• D. The point $(1,0)$ is always on the graph of the function

Answer 1

Answer: (A)

Consider the function $f(x)=b^x$. The domain of the function is set of all real numbers. Therefore, $x\in R$.
Now $y=b^x$,
$\log y=x\log$ b. Here, $b>1$ and the input of the $\log$ cannot be 0 . Hence $y>0$.
Therefore, the range of $f(x)>0$.
Now for $x\to \infty ,f(x)\to \infty$. Also, for $x\to -\infty ,f(x)\to 0$. Hence for large positive real numbers, the function tends to infinity.
Similarly fo negative numbers with large magnitudes, the function tends to be 0 .
Also, $f(1)=b^1=b$ and $f(0)=b^0=1$. Therefore, $(1,b)$ and $(0,1)$ lies on the graph of the function.