160 Key Concepts
Key Equations
General Form for the Translation of the Parent Logarithmic Function |
Key Concepts
- To find the domain of a logarithmic function, set up an inequality showing the argument greater than zero, and solve for x.
- The graph of the parent function
has an x-intercept at , domain , range , vertical asymptote x = 0, and- if b > 1, the function is increasing.
- if 0 < b < 1, the function is decreasing.
- The equation
shifts the parent function horizontally- left c units if c > 0.
- right c units if c < 0.
- The equation
shifts the parent function vertically- up d units if d > 0.
- down d units if d < 0.
- For any constant a > 0, the equation
- stretches the parent function
vertically by a factor of a if |a| > 1. - compresses the parent function
vertically by a factor of a if |a| < 1.
- stretches the parent function
- When the parent function
is multiplied by –1, the result is a reflection about the x-axis. When the input is multiplied by –1, the result is a reflection about the y-axis.- The equation
represents a reflection of the parent function about the x-axis. - The equation
represents a reflection of the parent function about the y-axis.
- A graphing calculator may be used to approximate solutions to some logarithmic equations.
- The equation
- All translations of the logarithmic function can be summarized by the general equation
. - Given an equation with the general form
, we can identify the vertical asymptote x = –c for the transformation. - Using the general equation
, we can write the equation of a logarithmic function given its graph.