Q:

Which conclusion about f(x) and g(x) can be drawn from the table

Accepted Solution

A:
Answer:The conclusion that is true about f(x) and g(x) based on the table of values is:      The function f(x) and g(x) are reflections over the y-axis.     Step-by-step explanation:We know that the rule that describes the reflection over the y-axis is:         (x,y) → (-x,y)Hence, if we have a function f(x) as:[tex]f(x)=2^x[/tex]Then it's reflection over the y-axis is:[tex]f(-x)=2^{-x}\\\\\\f(-x)=(2^{-1})^x\\\\\\f(-x)=(\dfrac{1}{2})^x\\\\i.e.\\\\\\g(x)=(\dfrac{1}{2})^x[/tex]Hence, they are reflection over the y-axis.Also, we know that the exponential function of the type:                 [tex]y=ab^x[/tex]where a>0 is a increasing function if b>1and is a decreasing function if: 0<b<1Hence, f(x) is a increasing function and g(x) is a decreasing function.Also, the initial value of a function is the value of function when x=0when x=0 we see that both f(x)=g(x)=1i.e. Both f(x) and g(x) have same initial value.Also,by the graph we may see the relation.