if f(x) is an odd function and the graph of f(x) includes points in quadrant iv, which statement about the…
if f(x) is an odd function and the graph of f(x) includes points in quadrant iv, which statement about the graph of f(x) must be true? it includes points in quadrant i. it includes points in quadrant ii. it does not include points in quadrant i. it does not include points in quadrant ii.
Answer
Explanation:
Step1: Recall property of odd - functions
An odd function satisfies $f(-x)=-f(x)$. Geometrically, the graph of an odd - function is symmetric about the origin.
Step2: Analyze quadrant relationship
If a point $(x,y)$ lies in Quadrant IV, then $x>0$ and $y < 0$. For an odd function, if $(x,y)$ is on the graph, then $(-x,-y)$ is also on the graph. Since $(x,y)$ with $x>0,y < 0$ is in Quadrant IV, then the point $(-x,-y)$ with $-x<0$ and $-y>0$ is in Quadrant II.
Answer:
It includes points in Quadrant II.