Logarithmic Transformations

Front

What is the Range of the logarithmic function?

Back

All Real Numbers

Front

Describe the transformation of f(x) = log x to f(x) = 3log(x + 1) - 5.

Back

Vertical stretch by 3 and shift left 1 and 5 units down.

Front

What happens to the asymptote of y = log_2(x + 1)?

Back

It does not shift at all and remains at x = 0.

Front

What is the equation of the asymptote for the function y = log(x) + 1?

Back

x = -3.

Front

Match the graph with its equation: y = log_5 (x + 1) + 1.

Back

This graph shifts the basic log function left by 1 and up by 1.

Front

What is a logarithm?

Back

A logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base be raised to produce a given number?

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a certain value.

Front

What is the domain of the logarithmic function?

Back

The domain of the logarithmic function is x > 0.

Front

What does a vertical stretch of a logarithmic function do?

Back

It multiplies the output of the function by a factor greater than 1, making the graph steeper.

Front

What does a horizontal shift of a logarithmic function do?

Back

It moves the graph left or right along the x-axis.