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In elementary school, we learned about opposite operations such as addition and
subtraction, and multiplication and division. In both of these cases, one operation
"undoes" the other.
In this course, we'll begin to explore "opposite" function types. For example, think about a
quadratic function and its key features. What key features do you think its opposite
function will have? Why?

User Aaplmath
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The opposite of a quadratic function would be an inverse quadratic function. The key features of a quadratic function are a parabolic shape, a vertex, and a y-intercept. The opposite function, the inverse quadratic function, would have a hyperbolic shape with two branches, a horizontal asymptote, and an x-intercept. This is because the inverse of a quadratic function is a rational function, which can be represented by a fraction with a quadratic polynomial in the denominator. The denominator of the inverse quadratic function would be the quadratic polynomial that determines the shape of the function, resulting in the hyperbolic shape with a horizontal asymptote. The x-intercept of the inverse quadratic function corresponds to the y-intercept of the original quadratic function, and the vertex of the inverse quadratic function corresponds to the minimum or maximum point of the original quadratic function. Overall, the key features of the opposite function would be different from those of the original function, reflecting the inverse relationship between the two.

User Belens
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