Determine the family of curves represented by the equation y = ax^3 + bx.
Practice Questions
1 question
Q1
Determine the family of curves represented by the equation y = ax^3 + bx.
Cubic functions
Quadratic functions
Linear functions
Exponential functions
The equation y = ax^3 + bx represents a family of cubic functions where a and b are constants.
Questions & Step-by-step Solutions
1 item
Q
Q: Determine the family of curves represented by the equation y = ax^3 + bx.
Solution: The equation y = ax^3 + bx represents a family of cubic functions where a and b are constants.
Steps: 6
Step 1: Identify the equation given, which is y = ax^3 + bx.
Step 2: Recognize that 'a' and 'b' are constants, meaning they do not change.
Step 3: Understand that 'x' is the variable that can change, affecting the value of 'y'.
Step 4: Note that the term 'ax^3' indicates that this is a cubic function because it has 'x' raised to the power of 3.
Step 5: Realize that changing the values of 'a' and 'b' will create different curves, but they will all be cubic functions.
Step 6: Conclude that the equation represents a family of curves, all of which are cubic functions with different shapes based on the values of 'a' and 'b'.
