State whether each equation represents a linear, quadratic, or exponential function. Tell how you decided.

1. y = 9^3x + 4
2. 4x = 5 - y
3. y = 2x^2 + 23 – 14x

To determine whether each equation represents a linear, quadratic, or exponential function, we need to analyze the form and behavior of the equations.

1. y = 9^3x + 4:
This equation represents an exponential function. The presence of a variable in the exponent (3x) indicates exponential growth. Additionally, the base of the exponent (9) is constant. Exponential functions have a constant ratio of change, and the variable grows or decays exponentially.

2. 4x = 5 - y:
This equation represents a linear function. It is in the form of y = mx + b, where m is the slope (in this case, 4) and b is the y-intercept (in this case, 5). Linear functions have a constant rate of change and form a straight line when graphed.

3. y = 2x^2 + 23 – 14x:
This equation represents a quadratic function. The presence of the squared term (x^2) indicates a quadratic relationship. Quadratic functions have a parabolic shape when graphed and their rates of change are not constant.

By analyzing the form and behavior of each equation, we can determine whether they represent linear, quadratic, or exponential functions.