5.4E: Exercises - Graphs and Properties of Logarithmic Functions

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Mar 6, 2024
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- 5.4: Graphs and Properties of Logarithmic Functions
- 5.5: Applications of Exponential and Logarithmic Functions

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PROBLEM SET: GRAPHS AND PROPERTIES OF LOGARITHMIC FUNCTIONS

Questions 1 – 3: For each of the following functions

Sketch a reasonably accurate graph showing the shape of the graph of the function
State the domain
State the range
State whether the graph has a vertical asymptote or a horizontal asymptote and write the equation of that asymptote
Does the graph have an x-intercept or a y-intercept asymptote? Write the coordinates of the x-intercept or the y-intercept.

$y=\ln x$ Sketch the graph below	domain: ________ range: ________ Is the asymptote horizontal or vertical? _________ Equation of the asymptote: ________ Coordinates of x-intercept or y-intercept: ________
$y=\log x$ Sketch the graph below	domain: ________ range: ________ Is the asymptote horizontal or vertical? _________ Equation of the asymptote: ________ Coordinates of x-intercept or y-intercept: ________
$y=\log_{0.8} x$ Sketch the graph below	domain: ________ range: ________ Is the asymptote horizontal or vertical? _________ Equation of the asymptote: ________ Coordinates of x-intercept or y-intercept: ________

Questions 4 - 5: For the pair of inverse functions $y = e^x$ and $y = \ln x$

Sketch a reasonably accurate graph showing the shape of the graph of the function
State the domain
State the range
State whether the graph has a vertical asymptote or a horizontal asymptote and write the equation of that asymptote
Does the graph have an x-intercept or a y-intercept asymptote? Write the coordinates of the xintercept or the y-intercept.

$y=e^x$ Sketch the graph below	domain: ________ range: ________ Is the asymptote horizontal or vertical? _________ Equation of the asymptote: ________ Coordinates of x-intercept or y-intercept: ________
$y=\ln x$ Sketch the graph below	domain: ________ range: ________ Is the asymptote horizontal or vertical? _________ Equation of the asymptote: ________ Coordinates of x-intercept or y-intercept: ________

Questions 6-11: Match the graph with the function.

Choose the function from the list below and write it on the line underneath the graph.

Hint: To match the function and the graph, identify these properties of the graph and function

Is the function increasing decreasing?
Examine the asymptote
Determine the x or y intercept

$\mathrm{y}=3\left(2^{x}\right) \quad y=5\left(0.4^{x}\right) \quad y=\log _{2}(x) \quad y=\log _{1 / 2}(x) \quad y=3 e^{-0.6 x} \quad y=5 e^{0.3 x} \nonumber$

Function: ________

$5.7.4Function6.png$

Function: ________

$5.7.4Function7.png$

Function: ________

$5.7.4Function8.png$

Function: ________

$5.7.4Function9.png$

Function: ________

$5.7.4Function10.png$

Function: ________

$5.7.4Function11.png$

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PROBLEM SET: GRAPHS AND PROPERTIES OF LOGARITHMIC FUNCTIONS

PROBLEM SET: GRAPHS AND PROPERTIES OF LOGARITHMIC FUNCTIONS

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