Review on Exponential Functions

Describe the transformation if

 $f\left(x\right)=2^x$  is the parent function and $g\left(x\right)=3^{\left(x+2\right)}$   is the transformed function.

• Vertical translation up 2 units

• Horizontal translation right 2 units

• Horizontal translation left 2 units
  

• Vertical translation down 2 units

Tags

CCSS.HSF.BF.B.3

If  $f\left(x\right)=4^x$  is the parent function, what is the transformed function when translated 4 units to the left and 2 units down?

•  $g\left(x\right)=4^{\left(x-2\right)}-4$  

•  $g\left(x\right)=4^{\left(x+4\right)}-2$  

•  $g\left(x\right)=4^{\left(x-4\right)}+2$  

•  $g\left(x\right)=4^{\left(x+2\right)}+4$  

Tags

CCSS.HSF.BF.B.3

Select ALL of the transformations of  $g\left(x\right)=-2\cdot\left(3\right)^{\left(x-1\right)}$  if the parent function is  $f\left(x\right)=3^x$  

• Horizontal translation right 2 units

• Horizontal translation left 1 unit

• Reflection

• Vertical Stretch 

• Horizontal translation right 1 unit

Tags

CCSS.HSF.BF.B.3

The bacteria count in a heated swimming pool is 1,500 bacteria per cubic centimeter on Monday at 8 AM, and the count doubles each day. Which function correctly represents the number of bacteria per cubic centimeter after t days?

• 
  

  $P\left(t\right)=2^t+1500$
  

• $P\left(t\right)=1500\cdot2^t$
  

• $P\left(t\right)=2\cdot1500^t$

• $P\left(t\right)=2^{\left(x-1500\right)}$

Tags

CCSS.HSF.LE.A.2

What is the asymptote of the graph?

• $x=2$

• $y=0$

• $y=-1$

• $y=-2$

Tags

CCSS.HSF-IF.C.7D

What is the transformation of  $y=2^{\left(x+1\right)}-2$  if  $y=2^x$  is the parent function?

• Vertical translation up 2 units and Horizontal translation right 1 unit

• Vertical translation down 2 units and Horizontal translation left 1 unit

• Horizontal translation left 2 units and Vertical translation up 1 unit

• Horizontal translation right 2 units and Vertical translation down 1 unit

Tags

CCSS.HSF.BF.B.3

If $f\left(x\right)=2\cdot4^x$ , find  $f\left(2\right)$  .

• 32
  

• 16
  

• 4

• 64

Tags

CCSS.HSF-IF.C.8B

Given $f\left(x\right)=5^x$  , write a function that is reflected over the x-axis AND translated 4 units to the right.

•  $g\left(x\right)=5^{\left(x+4\right)}$  

•  $g\left(x\right)=5^{-\left(x-4\right)}$  

•  $g\left(x\right)=-\left(5\right)^{\left(x-4\right)}$  

•  $g\left(x\right)=-\left(5\right)^{\left(x+4\right)}$  

Tags

CCSS.HSF.BF.B.3

Which of the following are considered exponential growth? Select ALL that apply.

• 
• 
• 
• 
• 

Tags

CCSS.HSF-IF.C.7E

What is the horizontal asymptote of the function:  $f\left(x\right)=3\cdot7^x+2$  

•  $y=3$  

•  $y=7$  

•  $y=0$  

•  $y=2$  

Tags

CCSS.HSF-IF.C.7D