Problem 132
Question
What must be done to a function's equation so that its graph is reflected about the \(y\) -axis?
Step-by-Step Solution
Verified Answer
To reflect a function's graph about the y-axis, simply replace every \(x\) in the equation with \(-x\).
1Step 1: 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).
2Step 2: 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 \(f(-x) = (-x)^2\).
Other exercises in this chapter
Problem 132
a. Graph the functions \(f(x)=x^{n}\) for \(n=2,4,\) and 6 in a [-2,2,1] by [-1,3,1] viewing rectangle. b. Graph the functions \(f(x)=x^{n}\) for \(n=1,3,\) and
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Determine whether each statement makes sense or does not make sense, and explain your reasoning. My graph is decreasing on \((-\infty, a)\) and increasing on \(
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Use point plotting to graph \(f(x)=x+2\) if \(x \leq 1\)
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