4.5.1: Graphs and Properties of Logarithmic Functions (Exercises)
SECTION 4.5 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.
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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.
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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
\[\mathrm{y}=3\left(2^{x}\right) \quad y=5\left(0.4^{x}\right) \quad y=\log _{2}(x) \quad y=\log _{1 / 2}(x) \quad y=3 e^{-0.6 x} \quad y=5 e^{0.3 x} \nonumber \]
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