Logarithm Graph

f(x)=2ln(x+2)

Describe the asymptote

• Horizontal asymptote x = -2

• Horizontal asymptote x = 2

• Vertical asymptote x = -2

• Vertical asymptote x = 2

Find the Domain and Range

• Domain: (-∞, ∞)

  Range: ( -2, ∞)

• Domain: (-∞, ∞)

  Range: ( -∞, -2)

• Domain: ( -∞, -2)

  Range: (-∞, ∞)

• Domain: ( -2, ∞)

  Range: (-∞, ∞)

f(x)=¼ ln(x - 2) + 3

Describe the asymptote

• Horizontal asymptote x=2

• Horizontal asymptote x= -2

• Vertical asymptote x=2

• Vertical asymptote x= -2

f(x)=2ln(x+2)

Describe the transformation

• Vertical Stretch by 2, translation 2 units to the left

• Vertical Compression by 2, translation 2 units to the left

• Vertical Stretch by 2, translation 2 units to the right

• Vertical Compression by 2, translation 2 units to the right

Find the Domain and Range

• Domain: all real numbers

  Range: y > 2

• Domain: all real numbers

  Range: y > -2

• Domain: x > -2

  Range: all real numbers

• Domain: x > 2

  Range: all real numbers

f(x)=¼ ln(x - 2) + 3 Describe the transformation

• Vertical Stretch by 1/4, translation 2 units right, 3 units up

• Vertical Compression by 1/4, translation 2 units right, 3 units up

• Vertical Stretch by 1/4, translation 2 units left, 3 units up

• Vertical Compression by 1/4, translation 2 units left, 3 units up

Graph the logarithmic function y = log(x) on the coordinate plane.

• The graph of y = log(x) is a parabola opening upwards.

• The graph of y = log(x) is a curve that intersects the x-axis at (1, 0) and approaches negative infinity as x approaches 0.

• The graph of y = log(x) is basically the same as the graph of a square root .

• The graph of y = log(x) is a straight line passing through the origin.

• The graph of y = log(x) is almost exactly like the graph of y=10^x.

Identify the x-intercept of the logarithmic function y = log(x).

• (2,0)

• (3,0)

• (1,0)

• (10,0)

• No way to know since the base is unknown

Identify the key points on the graph of the logarithmic function y = log(x).

• (0,1) and (1,10)

• (1,0) and (2,1)

• (1,0) and (2.718, 1)

• (1,0) and (10,1)

• (1,0) and (3,1)

Write the equation for the graph.

• f(x) = log₂ (x-3)

• f(x)= 3 log₂(x)

• f(x) = log₂(x+3)

• f(x) = log₂(x) + 3

• f(x)= log₂(x³)