Quadratic: Domain and Range

Front

What is the definition of the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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What is the definition of the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to have a domain of all real numbers greater than or equal to -7 and less than 2?

Back

It means that the function accepts any x-value starting from -7 up to, but not including, 2.

Front

How do you determine the domain of a quadratic function?

Back

The domain of a quadratic function is typically all real numbers unless there are restrictions based on the context of the problem.

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Front

What is the vertex of a quadratic function and how does it relate to the range?

Back

The vertex is the highest or lowest point of the parabola. For a downward-opening parabola, the y-coordinate of the vertex gives the maximum value of the range.

Front

What is the significance of the leading coefficient in a quadratic function?

Back

The leading coefficient determines the direction of the parabola: if it's positive, the parabola opens upwards; if negative, it opens downwards.

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Changing 'a' affects the width and direction of the parabola: larger absolute values of 'a' make the parabola narrower, while smaller absolute values make it wider.

Front

What does it mean for a function to have a range of all real numbers greater than or equal to -6?

Back

It means that the function can produce any y-value starting from -6 and going upwards.