Question

Two exponential functions are shown in the table.
х
f(x)=2*
g(x)=
1
2
2
4
1
4
Which conclusion about f(x) and g(x) can be drawn from
the table?
O The functions f(x) and g(x) are reflections over the x-
axis.
O The functions f(x) and g(x) are reflections over the y-
axis.
O The function f(x) is a decreasing function, and g(x) is
an increasing function.
O The function f(x) has a greater initial value than g(x).
1
2
OT
1
2
1
2
1
1
2
1
4
-2.
4

Answer 1

Yep exponential functions are shown in the answer 2

Answer 2

The true statement about the exponential functions is (b) the functions f(x) and g(x) are reflections over the y-axis.

The functions are given as:

$f(x) = 2^x$

$g(x) = (\frac 12)^x$

Reflect function over the y-axis.

The rule of this transformation is:

$(x,y)\to (-x,y)$

So, we have:

$f(x) = 2^x$

$f'(x) = 2^{-x}$

Apply power rule of indices

$f'(x) = (\frac{1}{2})^x$

By comparison:

$g(x) = f'(x) = (\frac{1}{2})^x$

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

Read more about function transformation at:

https://brainly.com/question/1548871