Features of Functions + Function Algebra

What does f(x) + g(x) represent?

• The product of the outputs of two functions f and g for the same input x.

• The difference between the outputs of two functions f and g for the same input x.

• The sum of the outputs of two functions f and g for the same input x.

• The average of the outputs of two functions f and g for the same input x.

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What is a constant function?

• A function that varies its output based on the input.

• A function that always returns the same value, regardless of the input.

• A function that has no output for any input.

• A function that only returns positive values.

What is the significance of the vertex in a quadratic function?

• It represents the x-intercept of the function.

• It is the highest or lowest point on its graph, depending on the direction of the parabola.

• It indicates the slope of the function.

• It is the point where the function changes from increasing to decreasing.

What does it mean for a function to be decreasing?

• A function is increasing if, as the input values increase, the output values decrease.

• A function is constant if, as the input values increase, the output values remain the same.

• A function is decreasing if, as the input values increase, the output values decrease.

• A function is decreasing if, as the input values increase, the output values increase.

How do you evaluate a function?

• By substituting the input value into the function's equation and simplifying.

• By finding the derivative of the function.

• By graphing the function and identifying the intercepts.

• By multiplying the input value by a constant.

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What is the range of a function?

• The set of all possible input values (x-values) that the function can accept.

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

• The difference between the maximum and minimum values of the function.

• The slope of the function at a given point.

What does it mean for a function to be increasing?

• A function is increasing if, as the input values increase, the output values also increase.

• A function is increasing if the output values decrease as the input values increase.

• A function is increasing if it has a constant output regardless of the input values.

• A function is increasing if it oscillates between increasing and decreasing values.

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What is the domain of a function?

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

• The set of all possible output values (y-values) for which the function is defined.

• The range of values that a function can take.

• The maximum value that a function can achieve.

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

• By evaluating the function at x = 0.

• By finding the slope of the function.

• By setting y = 0 and solving for x.

• By determining the maximum value of the function.

What is the minimum value of a function?

• The maximum point on its graph, representing the largest output value.

• The lowest point on its graph, representing the smallest output value.

• The average value of the function over its domain.

• The point where the function is undefined.