Question

select all of the odd functions.

Explanation:

Step1: Recall Odd Function Graph Property

An odd function satisfies \( f(-x)=-f(x) \), so its graph is symmetric about the origin. This means for every point \((x,y)\) on the graph, \((-x,-y)\) is also on the graph.

Step2: Analyze \( t(x) \) Graph

Check symmetry about the origin. For the green graph \( t(x) \), if we take a point \((x,y)\), the corresponding \((-x,-y)\) seems to lie on the graph (visually, the left and right sides mirror over the origin).

Step3: Analyze \( j(x) \) Graph

The red graph \( j(x) \) appears symmetric about the y - axis (even function property, \( f(-x)=f(x) \)), not the origin. So it's not odd.

Step4: Analyze \( s(x) \) Graph

The blue graph \( s(x) \): Check symmetry. For a point \((x,y)\) on \( s(x) \), \((-x,-y)\) should be on it. Visually, the graph has origin - symmetry (e.g., the shape on the right of the y - axis and left of the y - axis are mirror images over the origin).

Step5: Analyze \( r(x) \) Graph

The orange graph \( r(x) \) is symmetric about the y - axis (even function), so not odd.

Answer:

The functions \( t(x) \) (green graph) and \( s(x) \) (blue graph) are odd functions.