Holt Algebra 2

7-7 Transforming Exponential

and Logarithmic Functions

Logarithmic Transformations

Holt Algebra 2

7-7 Transforming Exponential

and Logarithmic Functions

g(x) = 5 log x – 2

asymptote: x = 0

The graph of g(x) is a vertical stretch of the parent function f(x) = log x by a factor of 5 and a translation 2 units down.

Domain: (0, ∞)

Range: (-∞, ∞)

Holt Algebra 2

7-7 Transforming Exponential

and Logarithmic Functions

h(x) = ln(–x + 2)

asymptote: x = 2

The graph of h(x) is a reflection of the parent function f(x) = ln x across the y-axis and a shift of 2 units to the right.

Domain: (-∞, 2)

Range: (-∞, ∞)

Holt Algebra 2

7-7 Transforming Exponential

and Logarithmic Functions

p(x) = –ln(x + 1) – 2

asymptote: x = –1

The graph of p(x) is a reflection of the parent function f(x) = ln x across the x-axis 1 unit left and a shift of 2 units down.

Domain: (-1, ∞)

Range: (-∞, ∞)

Holt Algebra 2

7-7 Transforming Exponential

and Logarithmic Functions

Check It Out! Example 4

Write the transformed function when f(x) = log x is translated 3 units left and stretched vertically by a factor of 2.

g(x) = 2 log(x + 3)

When you write a transformed function, you may want to graph it as a check.

Holt Algebra 2

7-7 Transforming Exponential

and Logarithmic Functions

Logarithmic and Exponential Functions Transformation worksheet