Key Concepts
Key Equations
General Form for the Translation of the Parent Function |
Key Concepts
- The graph of the function has a y-intercept at , domain , range , and horizontal asymptote .
- If , the function is increasing. The left tail of the graph will approach the asymptote , and the right tail will increase without bound.
- If 0 < b < 1, the function is decreasing. The left tail of the graph will increase without bound, and the right tail will approach the asymptote .
- The equation represents a vertical shift of the parent function .
- The equation represents a horizontal shift of the parent function .
- Approximate solutions of the equation can be found using a graphing calculator.
- The equation , where , represents a vertical stretch if or compression if of 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.
- All translations of the exponential function can be summarized by the general equation .
- Using the general equation , we can write the equation of a function given its description.