which equation choice could represent the graph shown below? answer f(x)=(x + 5)(x^2 - 25) f(x)=(x - 5)(x^2…
which equation choice could represent the graph shown below? answer f(x)=(x + 5)(x^2 - 25) f(x)=(x - 5)(x^2 - 25) f(x)=x(x^2 - 25) f(x)=x(x^2 + 25)
Answer
Explanation:
Step1: Find the x - intercepts
The x - intercepts of the graph are the points where the graph crosses the x - axis. From the graph, the x - intercepts seem to be (x=- 5,0,5).
Step2: Check the factored - form of the functions for x - intercepts
For a function (y = f(x)), if (f(x)=(x - a)(x - b)(x - c)), then the x - intercepts are (x=a,x = b,x = c).
- For (f(x)=(x + 5)(x^{2}-25)=(x + 5)(x + 5)(x - 5)), the x - intercepts are (x=-5,5).
- For (f(x)=(x - 5)(x^{2}-25)=(x - 5)(x + 5)(x - 5)), the x - intercepts are (x=-5,5).
- For (f(x)=x(x^{2}-25)=x(x + 5)(x - 5)), setting (f(x)=0), we have (x=0) or (x + 5=0) or (x - 5=0), so the x - intercepts are (x=-5,0,5).
- For (f(x)=x(x^{2}+25)), setting (f(x)=0), we have (x = 0) (since (x^{2}+25=0) gives (x^{2}=-25) and no real - valued solutions).
Answer:
(f(x)=x(x^{2}-25))