Extra Practice: Logarithms Graphs and Transformations

Front

What is the domain of the function y=log₂(x+1)?

Back

The domain is (-1, ∞).

Front

What is the equation of the asymptote for the function y=log₂(x+1)?

Back

The asymptote is x = -1.

Front

Find the asymptote of the function y=log₁₀(x) - 6.

Back

The asymptote is x = 0.

Front

What kind of asymptotes do logarithmic functions have?

Back

Logarithmic functions have vertical asymptotes (x = 0).

Front

Write the equation of the function f(x)=log(x+5)-6 after translating 3 units left and 2 units up.

Back

The new function is f(x)=log(x+8)-4.

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

How do you find the vertical asymptote of a logarithmic function?

Back

Set the argument of the logarithm to zero and solve for x.

Front

What is the general form of a logarithmic function?

Back

The general form is y = log_b(x - h) + k, where (h, k) is the translation of the graph.

Front

What happens to the graph of y=log_b(x) when b > 1?

Back

The graph increases and passes through the point (1, 0).