Identify the family of curves represented by the equation y = a^x.
Practice Questions
Q1
Identify the family of curves represented by the equation y = a^x.
Exponential functions
Logarithmic functions
Polynomial functions
Trigonometric functions
Questions & Step-by-Step Solutions
Identify the family of curves represented by the equation y = a^x.
Step 1: Understand the equation y = a^x. Here, 'y' is the output, 'a' is a constant, and 'x' is the input.
Step 2: Recognize that 'a' must be a positive number for the function to be defined for all real numbers.
Step 3: Note that as 'x' changes, 'y' will change based on the value of 'a'.
Step 4: Realize that different values of 'a' (like 2, 3, or 0.5) will create different curves, but they all belong to the same family of functions called exponential functions.
Step 5: Conclude that the equation y = a^x represents a family of exponential functions where 'a' is a positive constant.
Exponential Functions – The equation y = a^x represents a family of exponential functions where 'a' is a positive constant, indicating that the function grows or decays exponentially based on the value of 'a'.
