Exponential and Logarithmic functions

Exponential and Logarithmic functions

 $y=a\cdot b^{\left(x-h\right)}+k$  

• What does a do?

• What does h do?

• What does k do?

• What constraints are there on b and why?

Poll

 $y=a\cdot b^{\left(x-h\right)}+k$ 

In this exponential function, the value of b can be negative.

• True

• False

Poll

 $y=a\cdot b^{\left(x-h\right)}+k$ 

In this exponential function, the value of b cannot be zero.

• True

• False

Poll

 $y=a\cdot b^{\left(x-h\right)}+k$ 

In this exponential function, the value of b can be 1

• True

• False

Multiple Choice

 $y=a\cdot b^{\left(x-h\right)}+k$ 

In this exponential function, what does the h value do

• Move the graph horizontally

• Move the graph vertically

• Stretch or Shrink the graph

• Flip the graph over the x axis.

Multiple Choice

As x → ∞ , f(x) →

• -4

• -3

• ∞

• -∞

Multiple Choice

As x → -∞ , f(x) →

• -4

• -3

• ∞

• -∞

Multiple Choice

What is the asymptote of y = 2^x - 3

• y = 0

• y = -3

• x = 0

• x = -3

Multiple Choice

What is the asymptote of y = 2^x ?

• y = 0

• x = 0

Multiple Choice

Is the pictured graph growth, decay, or linear or none?  

• Growth
• Decay
• Linear
• None

Multiple Choice

Is the pictured graph growth, decay, or linear or none?  

• Exponential Growth
• Exponential Decay
• Linear
• None

Multiple Choice

Is the graph linear, exponential or neither?

• Linear
• Exponential
• Neither

Multiple Choice

 $\log_6\left(\frac{1}{216}\right)$  

Evaluate.

• 3

• ¹/₃

• -¹/₃

• -3

Multiple Choice

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

• Horizontal shift left one unit
• Horizontal shift right one unit
• Vertical shift up one unit
• Vertical shift down one unit

Multiple Choice

What is the domain and range of
f(x) = log ₃ (x + 1)?

• D: (− ∞, ∞) R: (−1, ∞)
• D: (− ∞, ∞) R: (1, ∞)
• D: (−1, ∞) R: (− ∞, ∞)
• D: (1, ∞) R: (− ∞, ∞)

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Multiple Choice

Evaluate log₄1

• 1
• 0
• 4
• undefined

Multiple Choice

 $\log_93=?$  Evaluate

• 2

•  $\frac{1}{2}$  

• -2

•  $-\frac{1}{2}$  
  

Multiple Choice

log₅25 = ?

• 2
• 5
• 125
• 10

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Multiple Choice

Rewrite log_pt = m in exponential form.

• p^t = m

• t^m = p

• m^t = p

• p^m = t

Multiple Choice

What is the equation of the asymptote on the graph of   $y=\log_5\left(x+3\right)+5$ ? 

• x = -3

• x=5

• y= -3

• y=5

Multiple Choice

Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions 

Multiple Choice

Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions 

Multiple Choice

What is the correct transformed equation for the graph?

• y = log(x - 4)

• y = log(x) - 4

• y = log(x + 4)

• y = log(x) + 4

Multiple Choice

What is the correct transformed equation for the graph?

• y = log(x - 4)

• y = log(x) - 4

• y = log(x + 4)

• y = log(x) + 4