Question

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

Answer 1

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:

$f(x)=2^x$

Then it's reflection over the y-axis is:

$f(-x)=2^{-x}\\\\\\f(-x)=(2^{-1})^x\\\\\\f(-x)=(\dfrac{1}{2})^x\\\\i.e.\\\\\\g(x)=(\dfrac{1}{2})^x$

Hence, they are reflection over the y-axis.

• Also, we know that the exponential function of the type:

                $y=ab^x$

where a>0 is a increasing function if b>1

and is a decreasing function if: 0<b<1

Hence, 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=0

when x=0 we see that both f(x)=g(x)=1

i.e. Both f(x) and g(x) have same initial value.

Also,by the graph we may see the relation.