The given piecewise functions are;
[tex]f(x) = \begin{cases}
-x + 2 & \text{ } x < 0 \\
x^2 + 1 & \text{ } x > 0
\end{cases}[/tex] [tex]g(x) = \begin{cases}
x + 2 & \text{ } x < 0 \\
x^2 + 2 & \text{ } x > 0
\end{cases}[/tex]
Comparison and contrast of the above piecewise functions
Similarities
The similarities are;
1) Both piecewise functions are linear when x < 0.
2) Both piecewise functions are quadratic when x > 0.
3) The magnitude the slope of the linear part both function are equal.
4) The leading coefficient of the quadratic function are the same.
5) The y-intercept of the linear function are equal, therefore, the linear functions in f(x) and g(x) intersect on the y-axis.
6) The domain of the linear and quadratic functions are the same.
Contrasts
The contrasts (differences) in the function are;
1) The slope of the linear function of g(x) is positive and the slope of the linear function of f(x) is negative.
2) The y-intercept of the quadratic function in f(x) is +1, while the y-intercept of the quadratic function in g(x) is +2.
3) The quadratic function in f(x) and g(x) have graphs that do not intersect.
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