which properties are present in a table that represents a logarithmic function in the form y = log_b x when…

which properties are present in a table that represents a logarithmic function in the form y = log_b x when b > 1? i. the y - values are always increasing or always decreasing. ii. the point (0, 1) exists in the table. iii. the y - values will decrease rapidly as the x - values approach zero. iv. there will only be one x - value in the table with a y - value of zero. o i only o i and ii only o i, iii, and iv o ii and iii only

which properties are present in a table that represents a logarithmic function in the form y = log_b x when b > 1? i. the y - values are always increasing or always decreasing. ii. the point (0, 1) exists in the table. iii. the y - values will decrease rapidly as the x - values approach zero. iv. there will only be one x - value in the table with a y - value of zero. o i only o i and ii only o i, iii, and iv o ii and iii only

Answer

Explanation:

Step1: Analyze property I

For the logarithmic function $y = \log_{b}x$ with $b>1$, the function is increasing. As $x$ increases, $y$ increases and as $x$ decreases, $y$ decreases. So property I is correct.

Step2: Analyze property II

For the function $y=\log_{b}x$, when $x = 0$, $\log_{b}0$ is undefined. When $x = 1$, $y=\log_{b}1=0$. So the point $(0,1)$ does not exist in the table and property II is incorrect.

Step3: Analyze property III

As $x\rightarrow0^{+}$ for $y = \log_{b}x$ with $b > 1$, $y\rightarrow-\infty$. So the $y -$values decrease rapidly as the $x -$values approach zero. Property III is correct.

Step4: Analyze property IV

Set $y = 0$, then $0=\log_{b}x$. By the definition of logarithms, $x = b^{0}=1$. So there is only one $x -$value (i.e., $x = 1$) for which $y = 0$. Property IV is correct.

Answer:

C. I, III, and IV