Algebra 2 Pre/Post-Assessment-Unit 2

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What is interval notation?

Back

Interval notation is a mathematical notation used to represent a range of values. It uses parentheses and brackets to indicate whether endpoints are included or excluded. For example, (a, b) means all numbers between a and b, excluding a and b, while [a, b] includes both endpoints.

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How do you determine where a function is positive?

Back

To determine where a function is positive, you need to find the intervals on the x-axis where the function's output (y-value) is greater than zero. This often involves analyzing the function's graph or solving inequalities.

Front

What does it mean for a function to have a maximum value?

Back

A function has a maximum value at a point where the function reaches its highest output compared to nearby points. This can be found using calculus (derivatives) or by analyzing the function's graph.

Front

How can you find the constant intervals of a function?

Back

To find the constant intervals of a function, look for sections of the graph where the output (y-value) does not change as the input (x-value) varies. This means the function's derivative is zero in those intervals.

Front

What is the significance of f(2) in a function?

Back

f(2) represents the output of the function when the input is 2. It is a specific value that can be found by substituting x=2 into the function's equation.

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How do you solve for x when f(x) equals a specific value?

Back

To solve for x when f(x) equals a specific value, set the function equal to that value and solve the resulting equation for x. This may involve algebraic manipulation or graphing.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints (e.g., (a, b)), while closed intervals do include their endpoints (e.g., [a, b]). This affects how we express ranges of values in interval notation.

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What is a function's range?

Back

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

Front

What is the role of the x-axis in analyzing functions?

Back

The x-axis represents the input values of a function. Analyzing the x-axis helps determine where the function is positive, negative, constant, or has specific values.

Front

How can you graph a function to find its maximum value?

Back

To graph a function, plot points based on input-output pairs and connect them smoothly. The highest point on the graph represents the maximum value of the function.