Question

The value of an art piece since 2010 is modeled by the function f(x)=12,500(1.12)^x

According to the function, the value of the art piece in 2010 is

A. $11,000

B. $12,500

C. $14,000
Answer
and it

A. increases

B. decreases

by a rate of ________ every year.

A. 0.12%

B. 0.88%

C. 12%

D. 88%
Answer
and it

A. increases

B. decreases

by a rate of ________ every year.

A. 0.12%

B. 0.88%

C. 12%

D. 88%

answer both
Answer
Let f(x)=2^x and g(x)=−f(x−1) . Identify the transformations of f(x).


Select all that apply.

Shifted down 1 unit

Shifted right 1 unit

Shifted left 1 unit

Shifted up 1 unit

Reflected over the x-axis

Reflected over the y-axis
Answered by GPT 3.5
B. $12,500
Answered by GPT 3.5
C. 12%
Answered by GPT 3.5
The value of the art piece increases by a rate of 12% every year.

So the answers are:

A. 0.12% (for the increase each year)

C. 12% (annual rate of increase)
Answered by GPT 3.5
Given functions:

f(x) = 2^x
g(x) = -f(x-1)

Transformations of f(x) when considering g(x) (which is -f(x-1)):
1. Shifted down 1 unit (from the minus sign before f(x))
2. Shifted right 1 unit (from the +1 inside the function)
3. Reflected over the x-axis (from the minus sign)

So the transformations of f(x) are:
- Shifted down 1 unit
- Shifted right 1 unit
- Reflected over the x-axis

The other options are not applicable to the function g(x) obtained from f(x).