Question

39Two exponential functions are shown in the table.XXf(x)=2xg(x)=4210-1-2Mark this and return21111124NIN|12|--IN2TIME REMAINING59:1710Which conclusion about f(x) and g(x) can be drawnfrom the table?O The functions f(x) and g(x) are reflections over the x-axis.The functions f(x) and g(x) are reflections over the y-axis.The function f(x) is a decreasing function, and g(x) isan increasing function.The function f(x) has a greater initial value than g(x).

Answer 1

The form of the exponential function is

`h(x)=ab^x`

a is the initial amount

b is the growth/decay factor

If

`b>1`

Then the function is growth (increasing)

`0Then the function is decay (decreasing)<p></p><p>Since the given functions are</p>[tex]\begin{gathered} f(x)=2^x\rightarrow(1) \\ g(x)=((1)/(2))^x\rightarrow(2) \end{gathered}`

Compare function (1) by the form above, then

a = 1

b = 2

Since b > 1, then

f(x) is an increasing function

compare function (2) by the form above, then

a = 1

b = 1/2

Since 0 < b < 1, then

g(x) is a decreasing function