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Chapter 1: Problem 72

Determine whether the statement is true or false. Justify your answer. The graph of \(y=-f(x)\) is a reflection of the graph of \(y=f(x)\) in the \(y\) -axis.

Short Answer

Expert verified
The statement is false.

Step by step solution

01

Understanding the concept

Reflecting a graph generally involves changing the sign in the function to flip it in a certain direction. Flipping a graph in the x-axis is achieved by changing the sign of the whole function, i.e., -f(x). But if we want to flip a graph in the y-axis, we change the sign of the x inside the function i.e., f(-x). So the given exercise is talking about a flip or reflection in the x-axis, not y-axis.
02

Determine whether the statement is true or false

Based on the understanding drawn from step 1, it can be concluded that the statement 'The graph of \(y=-f(x)\) is a reflection of the graph of \(y=f(x)\) in the \(y\)-axis.' is false because the graph of \(y=-f(x)\) is a reflection of the graph of \(y=f(x)\) in the \(x\)-axis, not the \(y\)-axis.

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