which properties are present in a table that represents an exponential function in the form $y = b^x$ when…

which properties are present in a table that represents an exponential function in the form $y = b^x$ when $b > 1$?\ni. as the x-values increase, the y-values increase.\nii. the point (1, 0) exists in the table.\niii. as the x-values increase, the y-values decrease.\niv. as the x-values decrease, the y-values decrease, approaching a singular value.\n\n○ i and iv\n○ i and ii\n○ ii and iii\n○ iii only

which properties are present in a table that represents an exponential function in the form $y = b^x$ when $b > 1$?\ni. as the x-values increase, the y-values increase.\nii. the point (1, 0) exists in the table.\niii. as the x-values increase, the y-values decrease.\niv. as the x-values decrease, the y-values decrease, approaching a singular value.\n\n○ i and iv\n○ i and ii\n○ ii and iii\n○ iii only

Answer

Explanation:

Step1: Analyze Property I

For $y = b^x$ where $b>1$, as $x$ increases, $b^x$ grows. For example, if $b=2$, $x=1$ gives $2^1=2$, $x=2$ gives $2^2=4$. So $y$ increases with $x$.

Step2: Analyze Property II

Substitute $x=1$ into $y = b^x$: $y = b^1 = b>1$, so the point is $(1, b)$ not $(1,0)$. This property is false.

Step3: Analyze Property III

Since $b>1$, as $x$ increases, $b^x$ increases, not decreases. This property is false.

Step4: Analyze Property IV

As $x$ decreases (moves to negative infinity), $y = b^x = \frac{1}{b^{|x|}}$. As $|x|$ increases, $\frac{1}{b^{|x|}}$ approaches 0 (a singular value) and decreases towards it. This property is true.

Answer:

I and IV