Questions and Answers
Which expressions are factors of the function represented in the graph? Select all that apply.
What is the domain and range of the function represented by the graph?
Domain: (−∞, ∞), Range: [5, ∞)
Which statement is true about the function represented by the graph?
The function has a minimum of -16.
Which statement is true about the end behavior of the function represented by the graph?
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Which statements are true about the function represented by the points in the table?
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Which statements are true about the intercepts of the function? Select all that apply.
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Which graph represents the same function as provided in the table?
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Which graph matches the following description: The function is increasing over the interval (−∞, 1) and decreasing over the interval (1, ∞), has a maximum of 3, and a y-intercept of (0, 2)?
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What are the x- and y-intercepts of the function f(x) = x^2 − 9x − 36?
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Which statement correctly describes the end behavior of the function f(x) = −x^2 + 3x + 12?
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What are the coordinates of the vertex of the following function f(x) = x^2 − 18x + 88?
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Which expression correctly describes the range of the function f(x) = (x + 12)^2 + 9?
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Which graph represents the same function as f(x) = x^2 − 4x − 5?
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Which function rule correctly describes the function represented in the graph?
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What equation represents the combined area of the pool and the deck?
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Which equation represents the height of the rubber band during the seconds after it is shot?
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Which measures are possible widths for Max's garden? Select all that apply.
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How long does it take the marshmallow to hit the ground, where h = 0?
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Which answer correctly explains the domain and range of the given situation?
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Match each question with the value that correctly answers the question.
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Which graph has the most appropriate labels and scales to graph the equation?
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Match the following questions with their respective values regarding Emily shooting an arrow upward with a bow.
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Study Notes
Factors of Functions
- Factors of the function graphed include (x - 1) and (x + 4).
Domain and Range
- The domain of the function is (−∞, ∞).
- The range of the function is [5, ∞).
Minimum Value
- The function has a minimum value of -16.
End Behavior of Functions
- For the given graph, as x approaches −∞, f(x) approaches ∞; as x approaches ∞, f(x) approaches ∞.
Minimum of Quadratic Functions
- The function depicted has a minimum value, approximately -7.25.
Intercepts of Functions
- The x-intercepts are (1, 0) and (−2, 0).
- The y-intercept is (0, −2).
Graph Representation
- A specific graph can represent the quadratic function indicated in the table.
Characteristics of Graphs
- A function increases over the interval (−∞, 1) and decreases over (1, ∞).
- It has a maximum value of 3 and a y-intercept at (0, 2).
X- and Y-Intercepts
- For the function f(x) = x^2 − 9x − 36, x-intercepts are (12, 0) and (-3, 0), while the y-intercept is (0, -36).
End Behavior of Specific Function
- For f(x) = −x^2 + 3x + 12, as x approaches both −∞ and ∞, f(x) approaches −∞.
Vertex of Quadratic Function
- The vertex of the function f(x) = x^2 − 18x + 88 is (9, 7).
Range of Transformed Functions
- For f(x) = (x + 12)^2 + 9, the range is 9 ≤ f(x) < ∞.
Graph Matching for Quadratic Equation
- The graph that corresponds to the function f(x) = x^2 − 4x − 5 can be identified based on graphical representation.
Function Rule Representation
- The function rule that describes the graph is f(x) = (x + 3)(x - 1).
Combined Area Equation
- The equation representing the combined area of a pool and deck is (9 + 2w)(12 + 2w) = 270.
Height Equation for Rubber Band
- The height of the rubber band after being shot is represented by h = −16t^2 + 26.4t + 15.
Possible Widths for a Garden
- Possible widths for Max's garden include 2 feet, 8 feet, and 9 feet.
Time for Objects to Hit Ground
- The marshmallow takes 2 seconds to reach the ground (h = 0).
Domain and Range in Context
- The domain ranges from 0 to 6.1 seconds, and the range is from 0 to 24.76 feet.
Questions and Values for Rocket
- Maximum height reached by the rocket is 24.76 feet.
- Time taken to reach this height is 2.55 seconds.
- Launching height of the rocket is 12 feet.
- It lands 6.1 seconds after launch.
Appropriate Graph Labels
- The graph selected must have the correct labels and scales for the equation.
Arrow Shooting Data
- The maximum height of the arrow is 90.69 feet, reached at 2.34 seconds.
- It is shot from a height of 2.8 feet and lands after 4.73 seconds.
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Description
Test your knowledge with these flashcards for Algebra 2A, focusing on Unit 2 concepts. Examine various graphs to identify factors, domains, and ranges of functions represented. Perfect for reviewing key algebra skills and preparing for exams.
