49. Which of these are not exponential relations? State reasons for all of your choices.
y = -2/3x - 2
y = 3 (x in place of square)
y = x²
y = -(x + 2)²
well, exponential functions are of the form y = a^x
where a is some positive number.
The "^" indicates an exponent when typing online
y = 3^x is exponential.That means the variable, in this case x, is in the exponent, not in the base. Thus y = x ^ 3 is NOT an exponential function.
To determine which of the given equations are not exponential relations, we need to understand the characteristics of exponential equations.
Exponential relations generally have the form y = a * b^x, where "a" and "b" are constants.
Let's evaluate each equation to see if it fits this form:
1. y = -2/3x - 2
This equation does not have the form of an exponential relation since it does not involve an exponent on the variable "x." Therefore, this equation is not an exponential relation.
2. y = 3 (x in place of square)
From the given equation, it is not clear what "(x in place of square)" means. However, if we assume it means "x squared", the equation becomes y = 3x^2. This equation is not an exponential relation since it involves the square of the variable "x" instead of being raised to a constant exponent.
3. y = x²
This equation does not have the form of an exponential relation. It is a quadratic equation since it involves the square of the variable "x". Quadratic equations have a squared term, which is not characteristic of exponential equations.
4. y = -(x + 2)²
Similar to the previous equation, this equation is also a quadratic equation. Since it involves the square of the variable "x", it is not an exponential relation.
To summarize:
- The equation y = -2/3x - 2 is not an exponential relation.
- The equation y = 3 (x in place of square) is not clear in terms of its intended meaning, but assuming it means "y = 3x^2", it is not an exponential relation.
- The equation y = x² is not an exponential relation.
- The equation y = -(x + 2)² is not an exponential relation.
None of the given equations are exponential relations.