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Chapter 2: Problem 132

What must be done to a function's equation so that its graph is reflected about the \(y\) -axis?

Short Answer

Expert verified
To reflect a function's graph about the y-axis, replace all the x variables in the equation with -x.

Step by step solution

01

Concept understanding

The reflection of a function about the y-axis means that if a function \(f(x)\) is reflected, the reflection will produce a new function, say \(g(x)\), such that \(g(-x) = f(x)\). This happens because the y-axis behaves like a mirror representing points on the left side in the right side and vice versa. Here -x represents the mirror image of x.
02

Operation on function

To reflect a function about the y-axis, you will replace all the x's in the equation with -x.
03

Result

As a result of this operation, the equation of the new function will be representative of the original function reflected about the y-axis.

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Most popular questions from this chapter

The toll to a bridge costs \(\$ 6.00 .\) Commuters who frequently use the bridge have the option of purchasing a monthly discount pass for \(\$ 30.00 .\) With the discount pass, the toll is reduced to \(\$ 4.00 .\) For how many bridge crossings per month will the cost without the discount pass be the same as the cost with the discount pass? What will be the monthly cost for each option? (Section \(1.3,\) Example 3 )

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