Question

Which one of the following is not correct for the feature of an exponential function given by$f\left(x\right)=b^x,b>1$?

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

Answer 1

The correct option is C

The point $\left(1,0\right)$ is always on the graph of the function

Explanation for the correct option.

Option C:

The given function is $f\left(x\right)=b^x,b>1$

Substituting the point $\left(1,0\right)$

$\Rightarrow$$y=b^x$

$\Rightarrow$$0=b^1$, Since $b>1,b^1\ne 0$

Hence, the correct option is C

Explanation for the incorrect options:

Option A: When the value of $x$is a large negative number, the function is $y=\frac{1}{b^x}$. Since $b>1,$the function approaches zero.

Option B: $x$can be any real number since $b>1,$

Option D: If the value of $x\ge 0$, the function will be of the form $y=b^x$. If the value of $x<0$, the function will be of the form $y=\frac{1}{b^x}$ since the value of $b>1.$ so in either case the range is positive real numbers.

Hence, the correct option is C