Nonlinear Function Problems

[Jhay493]

I have zero clue what to do here. At first I thought I was simply supposed to solve for the y values. Then I realized the choices don't match up at all. I've checked the answers already (2nd image) and can't seem to make sense of it. There is no explanation in the book. I'm lost on how to make any inferences. All I know is how they would look on the graph. For the first problem, both arms go down and for the 2nd problem, the left arm goes down and the right arm goes up. Can someone please explain how to get to those answers?

 

[tkhunny]

One must think about the nature of the graph. With f(x) = (x^2)/2, what is the nature of it? <== This is NOT the function in the text.

Starting from the negative x-axis and moving toward zero and continuing on to the positive x-axis...

We see that the value of f(x) is high and decreases toward zero. After getting to zero, it turns around and begins to increase. Thus, a first observation would be
1) For x < 0, Slope is negative
2) For x = 0, Slope = 0
3) For x > 0, Slope is positive.

That much information should get you started. Then , find a way to talk about magnitude and not just direction.

 

[Jhay493]

One must think about the nature of the graph. With f(x) = (-x^2)/2, what is the nature of it?

Starting from the negative x-axis and moving toward zero and continuing on to the positive x-axis...

We see that the value of f(x) is high and decreases toward zero. After getting to zero, it turns around and begins to increase. Thus, a first observation would be
1) For x < 0, Slope is negative
2) For x = 0, Slope = 0
3) For x > 0, Slope is positive.

That much information should get you started. Then , find a way to talk about magnitude and not just direction.

That makes a lot of sense. Thanks, I think I understand now!

 

[Aftab hassan]

Sir a>0 line is above the axis
2 a<0 line is below the axis
3 a=0 line become x-axis
How sir tkhunny ,your observation match with this

 

[tkhunny]

Sir a>0 line is above the axis
2 a<0 line is below the axis
3 a=0 line become x-axis
How sir tkhunny ,your observation match with this

Simple, turn the book upside down. It appears I was talking about about f(x) = ½x^2, not f(x) = -½x^2.

 

[mathdad]

Simple, turn the book upside down. It appears I was talking about about f(x) = ½x^2, not f(x) = -½x^2.

Question:

Can we say that all linear equations do not fall in the category of quadratic, cubic, and the rest because the highest degree is 1?

 

[tkhunny]

Question:

Can we say that all linear equations do not fall in the category of quadratic, cubic, and the rest because the highest degree is 1?

"linear" mean "degree 1" in a description of a function.

 

[mathdad]

"linear" mean "degree 1" in a description of a function.

Thank you. Interesting.