Graphing Functions

[Mitch885885]

Hey! I know you can't graph something on this website, but I was more interested in the order of operations....

Question: Graph f(x) = 2x^3 + 3x^2 - 3x - 2 using x-intercepts. the end behaviour of the function, and selected points on the graph.

I know that the end behaviour will end with the values of Y getting larger in a positive direction, but in order to obtain points of (x,y), do I sub in values so that f(x) = 0, factor the equation using the factor theorem or synthetic division, then solve for x?

Let x = 1, so that x-1 is a factor

2(1)^3 + 3(1)^2 - 3(1) - 2 = 0

After Synthetic the result is:
2x^2 + 5x + 2
= (2x + 1)(x + 2)
Therefore, we end up with : (x-1)(2x + 1)(x + 2).
So, would I graph the points: (1, 0), (-1/2, 0), (-2,0) ?

Lastly, how do I find the x-intercept? or find values for Y ?

Thanks for taking the time to read this!!

 

[stapel]

in order to obtain points of (x,y)...

To find points on the graph, pick x-values, plug them into the function, and simplify to find the corresponding y-values.

do I sub in values so that f(x) = 0, factor the equation using the factor theorem or synthetic division, then solve for x?

I'm sorry, but I don't understand the above. Are you "subbing in" known x-values, or are you "solving for" x-values?

Thank you.

Eliz.

Polynomial Graphs

 

[tkhunny]

That very last value from Synthetic Division is the value of the function.

Apply Synthetic Division for x = 2. The final value IS f(2).
Apply Synthetic Division for x = -12. The final value IS f(-12).