Exponential Data

If $ f(x) = 150 \times 2^{x} $ and $ g(x) = f(x) + 50 $, which transformation relates $ g $ to $ f $?

• g(x) is a horizontal shift of f(x) by 50 units.

• g(x) is a vertical shift of f(x) by 50 units upward.

• g(x) is a vertical stretch of f(x) by a factor of 50.

• g(x) reflects f(x) over the x-axis and shifts it up by 50 units.

Answer explanation

g(x) = f(x) + 50 indicates that g(x) is obtained by adding 50 to the output of f(x). This means g(x) is a vertical shift of f(x) by 50 units upward, making the correct choice the second option.

f

d

a

h

growth

1/2

decay

880

220

2

j

g

e

b

450

1/3

1350

decay

growth

3

2700x – 4050

150

For the table shown, the function in the form y = a(b)^x has an a value of ​ (a)   and a b value of ​ (b)  

• 72900

• 3

• 8100

• 1/3

• 24300

• 200

Given the table, determine the equation of the function. 

• y = 4(4)^x

• y = 4(¼)^x

• y = 4(x-0)² + 4

• y = 2(x-1)² + 16

Given the table, determine the equation of the function. 

• y = 2(½)^x

• y = 2x + 3

• y = -3x + 2

• y = 3(2)^x

Given the following table of values, construct the function that represents the sequence.

• y = 3(4)^x

• y = 3x + 4

• y = 4(3)^x

• y = 4x + 3

A tennis tournament begins with 128 players. At the end of round one, there will be 64 players. There are 32 players at the end of round 2 and 16 players remaining after round 3. Write the equation that best models this situation.

• y = -64x + 128

• y = 0.5x + 128

• y = 128(0.5)^x

• y = 128(2)^x

Identify the y-intercept (initial value) of the function f(x)=2(4)^x.

• 2

• 4

• (2)^x

• 8

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

• (.27)^x
• .27
• 13
• 3.51