Podcast
Questions and Answers
Which equation correctly represents the V-shaped graph that opens upwards?
Which equation correctly represents the V-shaped graph that opens upwards?
- $g(x) = -|x + 3|$
- $g(x) = |x - 3|$
- $g(x) = |x + 3|$ (correct)
- $g(x) = 2|x + 3|$
What is the range of the graph that shows a straight line starting at (1, 4) and going down towards (4, -0)?
What is the range of the graph that shows a straight line starting at (1, 4) and going down towards (4, -0)?
- $-4 ≤ f(x) ≤ 5$ (correct)
- $-4 ≤ f(x) ≤ 0$
- $0 ≤ f(x) ≤ 4$
- $-5 ≤ f(x) ≤ 5$
Which statement about the straight line graph starting at (1, 4) is FALSE?
Which statement about the straight line graph starting at (1, 4) is FALSE?
- The minimum value is at (4, -0).
- The graph has a negative slope.
- The maximum occurs at (1, 4).
- The graph is always negative. (correct)
At which point does the maximum value on the displayed graph occur?
At which point does the maximum value on the displayed graph occur?
What characterizes the behavior of the graph that starts at (1, 4)?
What characterizes the behavior of the graph that starts at (1, 4)?
Flashcards
Range of a function
Range of a function
The set of all possible output values (y-values) of a function.
Maximum of a function
Maximum of a function
A function's maximum value is the highest output value (y-value) it can achieve.
Minimum of a function
Minimum of a function
A function's minimum value is the lowest output value (y-value) it can achieve.
Always decreasing function
Always decreasing function
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Equation of a graph
Equation of a graph
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Study Notes
Function Equation
- The equation that represents the graph is g(x) = |x + 3|
Graph Analysis
- Range: The range is -4 ≤ f(x) ≤ 5. This means the y-values of the graph fall between -4 and 5, inclusive
- Domain: The domain is not 0 < x < 3. The domain is not explicitly stated but can be inferred from the graph. Based on the provided data for the domain, the correct domain is implied
- Trend: The graph is not always decreasing. A key characteristic of the graph is a single maximum point
- Maximum Point: The maximum value of the graph represented by the absolute value function is not at (0, 5). Based on the given graph, the maximum occurs at a specific point of the graph.
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Description
This quiz explores the function g(x) = |x + 3|, focusing on its graph characteristics including range, domain, and trends. Test your understanding of how to analyze the graph, identify its maximum point, and recognize the implications of the absolute value function.
