Algebra 2 | Unit 5 | Lesson 6: Symmetry in Equations | Practice Problems

Classify each function as odd, even, or neither. \(f(x)=3x^4+3\) \(f(x)=x^3-4x\) \(f(x)=\frac{1}{x^2+1}\) \(f(x)=x^2+x-3\)

• even

• odd

• even

• neither

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 \(h\).

The linear function \(f\) is given by \(f(x) = mx + b\). If \(f\) is even, what can you conclude about \(m\) and \(b\)?

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.

Write an expression for two of the graphs in terms of \(f(x)\).

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?