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 and understand the key features of the graphs of the functions x^4+x, x^4-x^2, and x^4, you can analyze the behavior of each function.

1. x^4+x: This function represents a fourth-degree polynomial with a positive coefficient for the x^4 term. The additional x term leads to an upward shift of the graph compared to the function x^4 alone. The key features of this graph include:
- The highest degree term is x^4.
- The graph will have a curvature similar to a "U" shape.
- The graph is shifted upwards compared to the function x^4.

2. x^4-x^2: This function also represents a fourth-degree polynomial, but it includes a negative x^2 term. This term creates a downward shift of the graph compared to the function x^4 alone. The key features of this graph are:
- The highest degree term is x^4.
- The presence of the negative x^2 term leads to a change in curvature compared to the function x^4.
- The graph is shifted downwards compared to the function x^4.

3. x^4: This function represents a fourth-degree polynomial without any additional terms. The key features of this graph are:
- The highest degree term is x^4.
- The graph will have a curvature similar to a "U" shape.
- There are no shifts or additional terms affecting the graph.

To visualize these graphs and compare them visually, you mentioned using a graphing calculator tool. The URL you provided seems to be a resource from Holt McDougal's online textbooks, but unfortunately, I cannot access specific URLs or external resources. However, you can follow these steps to graph these functions on your own graphing calculator or software:

1. Open the graphing calculator tool or software.
2. Enter the function x^4+x into the calculator and graph it.
3. Repeat step 2 for the functions x^4-x^2 and x^4.
4. Observe the resulting graphs and compare them based on the key features mentioned above.

Regarding your question about adding x^4+x and whether it would be the same as 2x^5, the answer is no. Adding x^4+x would not produce 2x^5. The sum of these polynomials is simply x^4+x.

You're welcome! If you have any more questions or need further explanations, feel free to ask!