Evaluating Functions

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Tags

CCSS.8.F.A.1

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How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function's equation and simplify.

Tags

CCSS.HSF.IF.A.2

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What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

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What does the vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola.

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How do you find the y-intercept of a function?

Back

To find the y-intercept of a function, set the input variable (x) to zero and solve for the output variable (y).

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What is the significance of the slope in a linear function?

Back

The slope of a linear function indicates the rate of change of the function; it represents how much the output changes for a unit change in the input.

Tags

CCSS.8.EE.B.5

Front

How can you determine the number of solutions to a quadratic equation?

Back

The number of solutions to a quadratic equation can be determined using the discriminant (b^2 - 4ac). If the discriminant is positive, there are two solutions; if zero, one solution; if negative, no real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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How do you interpret the meaning of a function in a real-world context?

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Interpreting a function in a real-world context involves understanding what the variables represent and how changes in one variable affect another.

Tags

CCSS.HSF.IF.B.4

Front

What is the difference between independent and dependent variables in a function?

Back

The independent variable is the input of the function (often x), while the dependent variable is the output (often y) that depends on the value of the independent variable.

Tags

CCSS.6.EE.C.9