Can you help with the characteristics of the function?
The parabola opens downward, at the top of the parabola off to the right side are the numbers (-1.25, 15.125) going on down the numbers are (0,12) the last numbers on this side are near the bottom (1.5, 0), then, on the left side directly opposite of (1.5,0) but in the inside of the parabola is the number (-4,0).
It's asking
1- As x approaches -infinity, f/x approaches where?
2- As x approaches infinity, f/x approaches where?
3- Domain in interval notation:
4- Range in interval notation:
5- x- intercept:
6- y- intercept
im sorry I know it's alot
No problem! Let's go through each of the characteristics of the function based on the given information:
1- As x approaches -infinity, f(x) approaches where?
- As x approaches negative infinity, the function f(x) approaches positive infinity because the parabola opens downward and the y-values keep increasing as x moves to the left.
2- As x approaches infinity, f(x) approaches where?
- As x approaches infinity, the function f(x) also approaches positive infinity because the parabola opens downward and the y-values keep increasing as x moves to the right.
3- Domain in interval notation:
- The domain of the function is all real numbers. In interval notation, this would be (-∞, ∞).
4- Range in interval notation:
- The range of the function based on the given points would be [0, 15.125] in interval notation.
5- x-intercept:
- The x-intercept of a parabola is where the function equals zero. In this case, the x-intercept is given as (1.5, 0).
6- y-intercept:
- The y-intercept of a function is where the graph intersects the y-axis. In this case, the y-intercept is given as (0, 12).
I hope this helps! Let me know if you need further clarification.
For the x intercept the only possible answer with the (1.5, 0)
Is (1.5, 0) & (-4, 0) could it be this answer since it is directly across from (1,5, 0) on the x axis I believe?
Yes, you are correct. The x-intercepts of the parabola are the points where the function equals zero, so in this case, the x-intercepts are (1.5, 0) and (-4, 0) since the y-value is zero at those points. Thank you for pointing that out. So the x-intercepts are (1.5, 0) and (-4, 0).
If you have any more questions or need further clarification, feel free to ask!
One more thing please for number 4 the range: the only answer with ( 0, 15.125) are ( - infinity, 15.125) and [-1.25 15.125] besides
the answer for the x intercept, unless I gave you the wrong information, it would be great if one day we can send a picture with our question.
I apologize for the confusion in my previous response. Thank you for pointing that out. Based on the given points, the correct range in interval notation would be [-∞, 15.125] since the highest y-value is 15.125 at ( -1.25, 15.125). So the range should be [-∞, 15.125].
And yes, it would definitely be helpful to send a picture with the question in order to provide more accurate assistance. If you have any more questions or need further clarification, feel free to ask. Thank you for your understanding.
Thank you so much
You're welcome! If you have any more questions in the future, feel free to ask. Have a great day!
Can you tell me what these [ ] mean?
In mathematics, the square brackets [ ] are typically used to denote intervals when representing sets of numbers.
For example:
- [a, b] represents a closed interval that includes all real numbers between a and b, including a and b.
- (a, b) represents an open interval that includes all real numbers between a and b, but excludes a and b.
- [a, b) represents a half-open interval that includes all real numbers between a and b, including a but excluding b.
- (a, b] represents a half-open interval that includes all real numbers between a and b, excluding a but including b.
- [-∞, ∞] represents the set of all real numbers.
I hope this explanation helps. Let me know if you need further clarification.