Lesson 6
Symmetry in Equations
Problem 1
Classify each function as odd, even, or neither.
- \(f(x)=3x^4+3\)
- \(f(x)=x^3-4x\)
- \(f(x)=\frac{1}{x^2+1}\)
- \(f(x)=x^2+x-3\)
Solution
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Problem 2
Here is a graph of a function \(f\) for \(0 \leq x \leq 5\).
- The function \(g\) is even and takes the same values as \(f\) for \(0 \leq x \leq 5\). Sketch a graph of \(g\).
- The function \(h\) is odd and takes the same values as \(f\) for \(0 \leq x \leq 5\). Sketch a graph of \(h\).
Solution
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Problem 3
The linear function \(f\) is given by \(f(x) = mx + b\). If \(f\) is even, what can you conclude about \(m\) and \(b\)?
Solution
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Problem 4
Here are the graphs of \(y = f(x)\) and \(y = f(x-1)\) for a function \(f\).
Which graph corresponds to each equation? Explain how you know.
Solution
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(From Unit 5, Lesson 2.)Problem 5
Write an expression for two of the graphs in terms of \(f(x)\).
Solution
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(From Unit 5, Lesson 3.)Problem 6
Here is a graph of the function \(f\) given by \(f(x) = x^3\).
- What happens if you reflect the graph across the \(x\)-axis and then across the \(y\)-axis?
- Is \(f\) even, odd, or neither?
Solution
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(From Unit 5, Lesson 5.)