20 two exponential functions are shown in the table.



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

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) is an increasing function.

the function f(x) has a greater initial value than g(x)

Answer-

The functions f(x) and g(x) are reflections over the y-axis.

Solution-

While reflecting any point with coordinates (x, y) over y-axis or x=0 line, the point shifts to (-x, y)

While reflecting any point with coordinates (x, y) over x-axis or y=0 line, the point shifts to (x, -y)

The given functions are,

Applying the formula for reflection of f(x) over y axis would be,

This is the equation for g(x)

Therefore, f(x) and g(x) are reflections over the y-axis.

The correct option is 2.

Step-by-step explanation:

The given functions are

It can be written as

When a function is reflected about the y-axis then

Since f(-x)=g(x), therefore functions f(x) and g(x) are reflections over the y-axis. Option 1 is incorrect and option 2 is correct.

The general exponential function is

Where, a is initial value and b is growth factor.

The function f(x) is increasing function because b=2>1.

The function g(x) is decreasing function because b=1/2<1.

Therefore option 3 is incorrect.

The initial value of both functions is 1.

Therefore option 4 is incorrect.

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step-by-step explanation:

1) is right

step-by-step explanation: