1) The graph which represents this is the graph at the bottom by the right
2) The graph which represents this is the graph at the bottom by the left
3) The graph which represents this is the graph at the top by the left
4) The graph which represents this is the graph at the top by the right
Step-by-step explanation:
We need to match the graphs with the statement. We will do so using their end behaviours and line movement.
1) The degree of the function is even, and the leading coefficient is negative
The ends of this graph will both be pointing down indicating that:
![\begin{gathered} As\text{ x }\rightarrow\text{ }\infty,\text{ f\lparen x\rparen }\rightarrow\text{ -}\infty \\ As\text{ x}\operatorname{\rightarrow}-\text{\infty},\text{ f}\operatorname{\lparen}\text{x}\operatorname{\rparen}\operatorname{\rightarrow}-\text{\infty} \end{gathered}]()
The graph which represents this is the graph at the bottom by the right
2) The degree of the function is even, and the leading coefficient is positive.
The ends of this graph will both be facing up indicating that:
![\begin{gathered} As\text{ x }\rightarrow\text{ }\infty,\text{ f\lparen x\rparen}\rightarrow\infty \\ As\text{ x}\operatorname{\rightarrow}-\text{\infty},\text{ f}\operatorname{\lparen}\text{x}\operatorname{\rparen}\operatorname{\rightarrow}\text{\infty} \end{gathered}]()
The graph which represents this is the graph at the bottom by the left
3) The degree of the function is odd, and the leading coefficient is negative. Odd replaced with on in the question.
The direction of the line will move from left to right indicating that:
![\begin{gathered} As\text{ x }\rightarrow\text{ }\infty,\text{ f\lparen x\rparen}\rightarrow-\infty \\ As\text{ x}\operatorname{\rightarrow}-\text{\infty},\text{ f}\operatorname{\lparen}\text{x}\operatorname{\rparen}\operatorname{\rightarrow}\text{\infty} \end{gathered}]()
The graph which represents this is the graph at the top by the left
4) The degree of the function is odd, and the leading coefficient is positive.
The direction of the line will move from right to left indicating that:
![\begin{gathered} As\text{ x }\rightarrow\text{ }\infty,\text{ f\lparen x\rparen}\rightarrow\infty \\ As\text{ x}\operatorname{\rightarrow}-\text{\infty},\text{ f}\operatorname{\lparen}\text{x}\operatorname{\rparen}\operatorname{\rightarrow}\text{\infty} \end{gathered}]()
The graph which represents this is the graph at the top by the right