Graphing Logarithms + Review

Front

What is the transformation of the logarithmic function \( f(x) = \log(x + 3) - 1 \)?

Back

Left 3, down 1.

Front

Describe the transformation of \( y = \ln(x) \) that gives the graph for \( y = \ln(x + 7) \).

Back

Horizontal translation 7 left.

Front

What is the asymptote for the logarithmic function \( f(x) = \log(x - 1) \)?

Back

x = 1.

Front

How has the graph transformed? Red is parent graph, Blue is transformation.

Back

Left 2, up 4.

Front

What is the parent function of logarithmic functions?

Back

The parent function is \( f(x) = \log(x) \).

Front

What is the domain of the logarithmic function \( f(x) = \log(x) \)?

Back

The domain is \( x > 0 \).

Front

What is the range of the logarithmic function \( f(x) = \log(x) \)?

Back

The range is all real numbers, \( (-\infty, \infty) \).

Front

What does a vertical shift of a logarithmic function do to its graph?

Back

It moves the graph up or down without affecting its shape.

Front

What does a horizontal shift of a logarithmic function do to its graph?

Back

It moves the graph left or right without affecting its shape.

Front

What is the effect of a negative sign in front of a logarithmic function, such as \( f(x) = -\log(x) \)?

Back

It reflects the graph across the x-axis.