# Sketch a possible graph of a function, f that has following properties ?

## Homework Statement

The graph of f goes through the origin; f is increasing at an increasing rate on the interval (0,1) and at a decreasing rate on (6, Infinity); f is constant on the interval (2,4); f is decreasing at an increasing rate for all other positive values of x; f(1)=2, f(3)=1, f(6)=-2, f has intercepts at x=0,5,7; f is an odd function.

## The Attempt at a Solution

I can understand the question, however, I don't know how to do this question.....Can anyone help me?

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They simply want you to draw the graph given the information. For instance, you know the graph has a point (0,0) because it says that it goes through the origin. You also know that it is increasing from (0,1) and decreasing from (6, infinity). It's also constant (a flat line) from (2,4) and so on. You could start by thinking about how these characteristics affect the graph of some function, maybe plot the given points of f(1), f(3), f(6)

Mark44
Mentor
They simply want you to draw the graph given the information. For instance, you know the graph has a point (0,0) because it says that it goes through the origin. You also know that it is increasing from (0,1) and decreasing from (6, infinity).
No, the graph is still increasing on (6, infinity), but at a decreasing rate. The phrases "increasing at an increasing rate" and "increasing at a decreasing rate" are directly related to both the first and second derivatives. Being that this question is posted in the Precalc section, it might be that the OP is not aware of derivatives.
It's also constant (a flat line) from (2,4) and so on. You could start by thinking about how these characteristics affect the graph of some function, maybe plot the given points of f(1), f(3), f(6)

I didn't even notice that it said "increasing at an increasing rate". My apologies. The idea is still the same, sketch generic graph which meets the listed criteria.