How can you distinguish between and exponential function y =3x, from a linear function y =3x and from a quadratic function y =3x2?

Nvm I got it

you use the proper notation.

linear: 3x
polynomial: 3x^2
exponential: 3^x

To distinguish between an exponential function, a linear function, and a quadratic function, you can look at the form of the equation and the relationship between the variables.

1. Exponential function: y = 3x
An exponential function is characterized by a variable in the exponent, typically written as y = ab^x, where 'a' and 'b' are constants. In this case, y = 3x can be considered an exponential function with a base of 3. The value of 'x' acts as an exponent, causing the values of 'y' to grow exponentially as 'x' increases.

2. Linear function: y = 3x
A linear function is characterized by a constant rate of change, meaning the relationship between 'x' and 'y' is a straight line. In this case, y = 3x represents a linear function with a slope of 3. For every unit increase in 'x', 'y' increases by 3 units.

3. Quadratic function: y = 3x^2
A quadratic function is characterized by a variable raised to the power of two ('x^2'). The equation y = 3x^2 can be considered a quadratic function. The graph of a quadratic function is a parabola, and the shape of the graph helps distinguish it from linear or exponential functions.

In summary, to distinguish between these functions, look for the presence of variables in the exponent (exponential), a constant rate of change (linear), or a variable raised to the power of two (quadratic). Additionally, observing the shape of the graph can provide further clarity.