HW Log Characteristics

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or intersects. For example, in the function y = log10(x + 3), the vertical asymptote is x = -3.

Front

What transformation is applied to the graph of y=ln(x) to obtain y=ln(-x)?

Back

The graph of y=ln(x) is reflected over the y-axis to obtain y=ln(-x).

Front

What does a vertical stretch by a factor of 7 do to the graph of y=ln(x)?

Back

A vertical stretch by a factor of 7 multiplies the output of the function by 7, making the graph steeper.

Front

Write the equation of the function after a vertical stretch by a factor of 2 and a translation 5 units to the right from f(x)=3log(x+4).

Back

g(x)=6log(x-5)+4.

Front

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

Back

The domain of y=log2(x+1) is (-1, ∞), meaning x must be greater than -1.

Front

What is the effect of reflecting a graph over the x-axis?

Back

Reflecting a graph over the x-axis inverts the y-values, changing positive values to negative and vice versa.

Front

How does a horizontal translation of 3 units to the left affect the function y=log(x)?

Back

The new function will be y=log(x+3), shifting the graph left by 3 units.

Front

What is the vertical compression by a factor of 1/2?

Back

A vertical compression by a factor of 1/2 reduces the height of the graph, making it flatter.

Front

What is the range of the function y=log(x)?

Back

The range of y=log(x) is (-∞, ∞), meaning it can take any real number value.

Front

What is the base of the logarithm in the function y=log10(x)?

Back

The base of the logarithm in y=log10(x) is 10.