1) True
2) False
3) True
4) False
5) False
Analyzing the table and the function g(x)= -12(1/3)^x
We can see that:
The y-intercept is given when x=0
So, (0, -12) and :
[tex]\begin{gathered} g(x)=-12(\frac{1}{3})^x \\ g(0)=-12(\frac{1}{3})^0 \\ g(0)=-12(1) \\ g(0)\text{ =-12} \end{gathered}[/tex]1) So both functions have the same y-intercept (y= -12).
Checking the second option:
[tex]\begin{gathered} g(0)\text{ =-12} \\ g(1)=-12(\frac{1}{3})^1,\text{ g(1)=-4} \\ g(2)=-12(\frac{1}{3})^2=-\frac{12}{9}=-\frac{4}{3} \\ g(3)\text{ =-0.44} \\ g(4)=-0.142 \\ g(-1)\text{ =-}36 \end{gathered}[/tex]2)So, as we can see both functions are increasing on this interval ([0,4], but not in every interval of x. False, since g(x) is a decreasing function.
3) For f(x) and g(x) this is true. since according to this graph we can see that the end behavior
Notice that as x approaches -∞, f(x) approaches -∞ as well as g(x). True
4) That's false too since both functions approach different values as x approaches infinity.
5) No, they do not have the same x-intercept. f(x), has x=2, and g(x) no.
[tex]\begin{gathered} g(x)=-12(\frac{1}{3})^x^{}_{} \\ 0=-12(\frac{1}{3})^x \\ \frac{0}{-12}=-\frac{12}{-12}(\frac{1}{3})^x \\ 0=(\frac{1}{3})^x \\ No\text{ solution in R} \end{gathered}[/tex]
