Which of the following describes the function x3 − 8?
2 answers:
Answer:
Option (a) is correct.
The degree of the function is odd, so the ends of the graph continue in opposite directions. Because the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.
Step-by-step explanation:
Given : Function
We have to choose out of given options that correctly describes the given function .
Consider the given function
Degree is the highest power of the function. Since, the given function has degree 3. So, it is odd.
So, The graph will be in opposite direction.
Also, The leading coefficient is 1 (coefficient of highest degree) and positive so the left side of the graph continues down the coordinate plane and the right side continues upward.
Also, The graph shifts 8 units downward from the origin.
Thus, Option (a) is correct.
The degree of the function is odd, so the ends of the graph continue in opposite directions. Because the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.
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Answer:
Step-by-step explanation:
To sketch a quadratic function we need two things:
1) Nature of the curve
2) Vertex
3) y-intercept
The completing square form of the quadratic equation is:
where,
a represents the nature of the graph it can be maximum or minimum , meaning, if a > 0 then minimum(u shaped curve/happy face) and if a < 0 then maximum(n shaped curve/sad face).
h represents the x-coordinate of the vertex.
k represents the y-coordinate of the vertex.
Now if we compare g(x) with our completing square form we get the following:
When we simply compare the following we get ,
a = 1 , which means a > 0 since 1 is greater than 0 the nature of the curve will be minimum(happy face/u shaped)
h = 4, which means the x-coordinate of the vertex is 4
k = 12, which means the y-coordinate of the vertex is 12
Now we have the nature of the curve, we have the vertex now all we need is the y-intercept.
For y-intercept:
For y-intercept meaning at which point will the graph cross the y-axis(0 , y)
For that we expand the formula and turn it into the standard quadratic equation form by using the formula (a - b)^2
now we compare with the standard quadratic form:
here c is the y-intercept and while comparing we can see that c = 28 ,
so the curve cuts the y-axis at (0 , 28)
So we have all the three things that we need to graph our function.
So we just plot the y-intercept , the vertex , and join the dots. Just a tip draw a dotted line on the x-coordinate of the vertex because the vertex point is also called as a turning point where the graph goes in the opposite direction just like a mirror reflection. I attached 2 images you can check them out. One is handmade(i know i suck at drawing but still xD) , one is sketched by online graphing calculator.
