Graphing Logarithmic Functions with Transformations

Front

What is the effect of a vertical compression by a factor of 1/2 on the graph of a logarithmic function?

Back

The graph is squeezed vertically towards the x-axis, making it less steep.

Front

What is the effect of translating a logarithmic function 4 units to the left?

Back

The entire graph shifts 4 units to the left along the x-axis.

Front

What is the domain of the function y=log_2(x+1)?

Back

The domain is (-1, ∞), meaning x must be greater than -1.

Front

What is the range of the function y=log_2(x+1)?

Back

The range is (-∞, ∞), meaning it can take any real number value.

Front

How do you write the equation of a logarithmic function after a vertical stretch by a factor of 2 and a translation 5 units to the right?

Back

The new function is g(x)=6log(x-5)+4.

Front

What is the end behavior of the function y=log_2(x+1) as x approaches infinity?

Back

As x approaches infinity, y approaches infinity.

Front

What happens to the graph of y=log(x) when you apply a horizontal stretch by a factor of 2?

Back

The graph becomes wider, stretching away from the y-axis.

Front

What is the effect of a vertical stretch by a factor of 3 on the function y=log(x)?

Back

The graph becomes steeper, stretching away from the x-axis.

Front

What is the transformation of the function y=log(x) when it is translated 2 units up?

Back

The new function is y=log(x) + 2.

Front

What is the vertical asymptote of the function y=log_2(x+1)?

Back

The vertical asymptote is at x = -1.