x^4+x
x^4-x^2
x^4
my.hrw/math06_07/nsmedia/tools/Graph_Calculator/graphCalc
I graphed all three, however I can't say what the key features of the graphs of these functions?? how do u compare these types of graph
ANSWER: can you add them like would x^4+x be the same as 2x^5
THANK YOU SOO MUCH!!
To compare the key features of the graphs of these three functions (x^4+x, x^4-x^2, x^4), you can analyze their polynomial forms.
1. x^4+x:
When you have a polynomial of the form x^n + x, the highest degree term is x^n. In this case, the highest degree term is x^4. Since the exponent is even, the graph will have a similar shape to a "U." This is because when x approaches positive or negative infinity, the function will tend towards positive infinity. Additionally, since there is a positive coefficient in front of the x-term, the graph will be shifted upward.
2. x^4-x^2:
Similar to the previous function, the highest degree term is x^4. Since the exponent is even, the graph will have a "U" shape. However, this time we have a negative coefficient in front of the x^2 term, which will affect the graph. The negative coefficient means that the graph will be reflected across the x-axis. This means that the right side of the "U" will be lower than the left side.
3. x^4:
In this case, we only have the term x^4 without any additional terms. The graph of this function will also have a "U" shape due to the even exponent. However, since there are no additional terms, the graph will not be shifted or reflected in any way. It will simply be a symmetric "U" shape centered at the origin.
So, to summarize:
- For x^4+x, the graph will be a "U" shape shifted upward.
- For x^4-x^2, the graph will be a "U" shape reflected across the x-axis, with the right side lower than the left side.
- For x^4, the graph will be a symmetric "U" shape centered at the origin.
Regarding your question about adding x^4+x to 2x^5, these two expressions cannot be directly combined because they have different terms with different degrees. They represent separate functions, and adding them would result in a different equation altogether. So, x^4+x and 2x^5 are not the same.
It seems like you have used a graphing calculator to plot these functions. The provided link appears to be a resource for a graphing calculator tool. Graphing calculators can help visualize the key features of various functions and equations, making it easier to analyze and compare them.