Question

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

Answer 1

For all the simple people like myself it’s B

Answer 2

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.

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)=((1)/(2))^x\\\\i.e.\\\\\\g(x)=((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.