Two exponential functions are shown in the table. Which conclusion about f(x) and g(x) can be drawn from
the table?
X
Х
f(x)=2*
g(x) =
2
4
1
4
1
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.
The function f(x) has a greater initial value than g(x).
1
2
1
0
-1
1
2
A-NI-
-2
4
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Given:

The two exponential functions are shown in the given table.

To find:

The correct conclusion about the functions f(x) and g(x).

Solution:

The given functions are:

The function g(x) can be written as:

It means the graphs of f(x) and g(x) are reflections over the y-axis. So, option B is correct.

Since , therefore the functions f(x) and g(x) are not the reflections over the x-axis. So, option A is incorrect.

The function f(x) is an increasing function because the base of the exponent is . The function g(x) is a decreasing function because the base of the exponent is . So, option C is incorrect.

At x=0 the value of f(x) is 1 and the value of g(x) is also 1. It means the functions has same initial values. So, option D is incorrect.

Therefore, the correct option is B.

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

if x = 1, then the answer is 3.5