10. Topic 14 Review

​Topic 14 Test Review

Logarithms

Multiple Choice

Find the inverse function of $$f\left(x\right)=5^x$$  

• $$f'\left(x\right)\ =\ \log_5x$$  

• $$f'\left(x\right)=\log_{5x}$$  

• $$f'\left(x\right)=5\log x$$  

• $$f'\left(x\right)=\log5x$$  

Multiple Choice

Graph $$\ln(x+1)$$  

Match

Match the following graphs with their domains

Domian: x > -2

Domian: x > 3

Domian: x > 0

Domian: x > 2

• Domian: x > -2

• Domian: x > 3

• Domian: x > 0

• Domian: x > 2

Match

Match the following log functions to their horizontal shift (which way will the asymptote shift)

• $$\ln\left(x\right)$$  

• $$\ln\left(x-4\right)$$  

• $$\ln\left(x+5\right)$$  

No Horizontal Shift

Shift Right

Shift Left

• No Horizontal Shift

• Shift Right

• Shift Left

Multiple Choice

What is the transformation of the logarithmic function $$f\left(x\right)=\log\ \left(x+3\right)-1$$  

• left 3, right 1

• right 3, down 1

• right 3, up 1

• left 3, down 1

Multiple Choice

Where is the vertical asymptote and what is the domain of this graph?

• asymptote x = 1 and domain

  (1, $$\infty$$  )

• asymptote y = 1 and domain

  (-1, $$\infty$$  )

• asymptote x = -1 and domain

  ( $$\infty$$ , 1)

• asymptote y = -1 and domain

  ( $$\infty$$ , 1)

Multiple Choice

Describe the transformations of f(x)= -log₂(x+1)

• left 1

• left one & reflected over the y-axis

• left one & reflected over the x-axis

• right one & reflected over the x axis

Multiple Choice

Classify the following graph.

• Exponential Growth
• Exponential Decay
• Logarithmic

Multiple Choice

What is the Asymptote?

• x=5

• x=0

• y=0

• x=1

Multiple Choice

Logarithms and Exponentials are what?

• parallel
• perpendiular 
• inverses
• congurent

Multiple Choice

Change the following exponential equation into a log equation:

$$2^5=32$$  

• $$\log_25=32$$  

• $$\log_{32}5=2$$  

• $$\log_232=5$$  

Multiple Choice

Write in exponential form.
log₂32 = 5

• 2^-5 = 32
• 2³² = 5
• 2⁵ = 32
• 32⁵ = 2