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What is the key difference between the graph of a linear relationship and the graph of a nonlinear relationship?
What is the key difference between the graph of an exponential relationship and the graph of a quadratic relationship?

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The main key difference between the graph of a linear relationship and the graph of a nonlinear relationship are linear relationship is the relation between variables which creates a straight line when spotted on a cartesian plane and linear relations have constant slope always.The key difference between the graph of an exponential relationship and the graph of a quadratic relationship is exponential relation is a mathematical function of the following form: f ( x ) = a x. where x is a variable, and a is a constant called the base of the function but quadratic relationship of the graph is the the standardized form of a quadratic equation is ax^2 + bx + c = 0,.

Answer:

Linear functions are in the form of [tex]y=mx+b[/tex] where 'm' is the slope and b is the y intercept. Linear functions are graphed as straight lines, whereas the graph for a non-linear relationship is curved. A non-linear relationship tells that if 'x' intercept changes this does not always make same change in the y variable.

The quadratic relationships are in the form [tex]y=ax^{2} +bx+c[/tex].  In quadratic functions the x is squared. The graph of quadratic equation is a parabola.

In exponential relationship, as the value of x increases, the value of f(x) also increases proving that the function is an increasing function. The inverse of an exponential function is a logarithmic function. The exponential is shown as :[tex]f(x)=b^{x}[/tex] where b > 0 and that b ≠ 1.