Explore: Transform Logarithmic Functions with Technology Solutions

Transform Logarithmic Functions with Technology Solutions

Transformations on logs, $y = a \log_{b} (x - h) + k$ , occur when the values of a, h, and k change, just as they do for other functions.
Use technology to transform logarithmic functions because many of the ordered pairs (or points) contain irrational numbers.
Then, create a sketch including the key details:
- asymptotes
- intercepts
- end behavior

Note

These transformations work on all types of logarithms: $\log_{b},$ common logs, and natural logs.

Write the equation, then sketch the graph.

Transform $y = \ln x$ by shifting the graph left two units and down four units.

$y = \ln (x + 2) - 4$

Describe the transformation of the functions f(x) to g(x).

$f (x) = e^{x} g (x) = \ln (x - 3) + 2$

$e \to \ln = inverse f (x) : a = 1, h = 0, k = 0 g (x) : a = 1, h = 3, k = 2$

g(x) is reflected over $y = x$ , shifted right 3 units, and shifted up 2 units from f(x).

To extend your learning, check out the More to Explore for this lesson.