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Chapter 1: 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, simply replace every \(x\) in the equation with \(-x\).

Step by step solution

01

Understanding function reflection

Reflection of a function graph simply means that the shape of the graph remains the same, but changes its direction. Reflection about the y-axis means that the graph remains the same, only the direction along the x-axis is reversed. In other words, for any point on the graph with coordinates (a,b), the reflected point will have coordinates (-a,b).
02

Modify the function's equation

To replicate the reflection of a graph about the y-axis, the x-values in the function should be replaced with their negatives. For instance if a function is given as \(f(x) = x^2\), then the function after reflection about the y-axis will be \(f(-x) = (-x)^2\).

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Most popular questions from this chapter

The regular price of a computer is \(x\) dollars. Let \(f(x)=x-400\) and \(g(x)=0.75 x\) a. Describe what the functions \(f\) and \(g\) model in terms of the price of the computer. b. Find \((f \circ g)(x)\) and describe what this models in terms of the price of the computer. c. Repeat part (b) for \((g \circ f)(x)\) d. Which composite function models the greater discount on the computer, \(f^{\circ}\) g or \(g \circ f\) ? Explain.

Here is the Federal Tax Rate Schedule \(X\) that specifies the tax owed by a single taxpayer for a recent year. (TABLE CANNOT COPY) The preceding tax table can be modeled by a piecewise function, where \(x\) represents the taxable income of a single taxpayer and \(T(x)\) is the tax owed: $$T(x)=\left\\{\begin{array}{ccc} 0.10 x & \text { if } & 0379,150 \end{array}\right.$$ Use this information to solve. Find and interpret \(T(50,000)\)

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