Understanding Graphs of Absolute Value Functions

The video tutorial explains how to graph the function f(x) and its absolute value counterpart f(|x|). It begins by introducing the concept and showing a table of values to highlight differences when x is negative. The tutorial then provides a graphical representation, explaining how the graph of f(|x|) is a reflection of f(x) across the y-axis for negative x values. The video concludes with an example to reinforce the concept, emphasizing the symmetry of f(|x|) across the y-axis.

What happens to the graph of f(x) when you graph f(|x|) for x < 0?

• It is reflected across the y-axis.

• It is reflected across the x-axis.

• It is shifted upwards.

• It remains unchanged.

In the table of values, how do f(x) and f(|x|) compare when x is non-negative?

• f(x) is always greater than f(|x|).

• f(x) and f(|x|) are the same.

• f(x) is always less than f(|x|).

• f(x) is the negative of f(|x|).

When x is negative, how is f(|x|) determined from f(x)?

• By doubling the value of f(x).

• By using the value of f(x) at the positive equivalent of x.

• By halving the value of f(x).

• By taking the negative of f(x).

What is the first step in graphing f(|x|) from f(x)?

• Ignore the part of the graph where x < 0.

• Double the values of f(x) for x > 0.

• Shift the graph to the right.

• Reflect the entire graph across the x-axis.

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How do you obtain the left part of the graph of f(|x|)?

• By reflecting the right part of f(x) across the y-axis.

• By shifting the graph of f(x) upwards.

• By rotating the graph of f(x) 180 degrees.

• By stretching the graph of f(x) horizontally.

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What property does the graph of f(|x|) always exhibit?

• No symmetry at all.

• Asymmetry across the y-axis.

• Symmetry across the y-axis.

• Symmetry across the x-axis.

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In the further graphical example, what is the first step to graph f(|x|)?

• Reflect the entire graph across the x-axis.

• Ignore the part of the graph where x < 0.

• Double the values of f(x) for x > 0.

• Shift the graph to the right.

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What is the result of reflecting the right part of f(x) across the y-axis?

• The graph is shifted upwards.

• The left part of the graph of f(|x|) is formed.

• The graph becomes a straight line.

• The graph is rotated 90 degrees.

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CCSS.HSF-IF.C.7D

What is the significance of the symmetry in the graph of f(|x|)?

• It shows that f(x) is a linear function.

• It indicates that f(x) is an even function.

• It confirms that f(x) is a periodic function.

• It demonstrates that f(x) is a quadratic function.

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What is the final takeaway about the graph of f(|x|)?

• It is always a circle.

• It is always symmetric across the y-axis.

• It is always symmetric across the x-axis.

• It is always a straight line.

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CCSS.HSF-IF.C.7A