Introduction to Logarithmic Function

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CCSS.HSF-IF.C.7E

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What value never changes in the logarithmic functions?

• Vertical asymptote

• Horizontal asymptote

• Domain

• Range

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Find the domain and range of:
f(x) = log₂(x)

• D: all real numbers
  R: y > 0

• Domain: all real numbers
  Range: all real numbers

• Domain: x > 0
  Range: all real numbers

• Domain: all real numbers
  Range: y < 0

Explain the behavior of the asymptote in a logarithmic function graph.

• The asymptote in a logarithmic function graph is a vertical line that the graph approaches but never touches.

• The asymptote in a logarithmic function graph is a horizontal line

• The asymptote in a logarithmic function graph is a point where the graph intersects

• The asymptote in a logarithmic function graph is a curve that the graph follows

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What is the general shape of a basic logarithmic function graph?

• Square

• Curve

• Circle

• Straight line

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How does changing the base of a logarithmic function affect its graph?

• Changing the base of a logarithmic function affects its graph by rotating it vertically.

• Changing the base of a logarithmic function affects its graph by changing the color of the graph.

• Changing the base of a logarithmic function affects its graph by shifting it horizontally.

• Changing the base of a logarithmic function affects its graph by stretching or compressing it horizontally.

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Describe the domain and range of a basic logarithmic function.

• Domain: All real numbers, Range: All real numbers

• Domain: All positive real numbers, Range: All real numbers

• Domain: All negative real numbers, Range: All real numbers

• Domain: All real numbers, Range: All positive real numbers

What is the x-intercept of a logarithmic function graph?

• The x-intercept of a logarithmic function graph is not defined, as logarithmic functions do not intersect the x-axis.

• The x-intercept of a logarithmic function graph is always 0.

• The x-intercept of a logarithmic function graph is a negative value.

• The x-intercept of a logarithmic function graph is at infinity.

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How can you determine the vertical asymptote of a logarithmic function graph?

• Look for the horizontal line where the argument of the logarithm is less than or equal to zero.

• Check if the function is continuous at x=0.

• Count the number of x-intercepts on the graph.

• Find the vertical line where the argument of the logarithm is less than or equal to zero.

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