Question

A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries 16, 8, 4, 2, 1.
Which exponential function is represented by the values in the table?

f(x) = One-half(4)x
f(x) = 4(4)x
f(x) = 4(one-half) Superscript x
f(x) = One-half (one-half) superscript x

Answer 1

Answer:

Given:

x: -2 -1 0 1 2

f(x): 16 8 4 2 1

To find:

Exponential which represents the values in the given table

Solution:

Let exponential function

f(x)=a^{x+c}f(x)=a

x+c

where c is constant.

Substitute x=0

f(0)=a^{c}f(0)=a

c

a^{c}=4a

c

=4

f(1)=a^{1+c}f(1)=a

1+c

a^{1+c}=2a

1+c

=2

\frac{a^c}{a^{1+c}}=2

a

1+c

a

c

=2

\frac{1}{a}=2

a

1

=2

a=\frac{1}{2}a=

2

1

4=(\frac{1}{2})^{c}4=(

2

1

)

c

2^{2}=2^{-c}2

2

=2

−c

By comparing we get

-c=2

\implies c=-2⟹c=−2

Now, the exponential function

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

2

1

)

x−2

Step-by-step explanation:

this is the answer I hope it helps you

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Answer 2

Answer:

f(x) = 4(one-half) Superscript x