Problem 73
Question
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If a point is on the \(y\) -axis, its \(x\) -coordinate must be 0
Step-by-Step Solution
Verified Answer
The statement 'If a point is on the \(y\) -axis, its \(x\) -coordinate must be 0' is true and needs no alteration.
1Step 1 Understanding the statement
The statement implies that any point which lies on the \(y\) -axis should have its \(x\) -coordinate as 0. In the Cartesian plane, the \(x\)-axis is horizontal and the \(y\)-axis is vertical. A point that lies on the \(y\)-axis can have any value for its \(y\)-coordinate, but its \(x\)-coordinate is always 0.
2Step 2 Evaluate the statement
Consider the claim in the statement. If any point is on the \(y\) -axis, then its x-coordinate is indeed 0. This is a fundamental fact about the Cartesian coordinate system.
3Step 3 Conclusion
Based on the observation in Step 2, the statement in the exercise is correct. Hence, there is no need to make any changes to it.
Other exercises in this chapter
Problem 73
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Describe how to use the graph of a one-to-one function to draw the graph of its inverse function.
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Find; a. \((f \circ g)(x)\) b. the domain of \(f \circ g\) $$f(x)=x^{2}+4, g(x)=\sqrt{1-x}$$
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Begin by graphing the square root function, \(f(x)=\sqrt{x} .\) Then use transformations of this graph to graph the given function. $$h(x)=\sqrt{-x+2}$$
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