•The x-intercepts of the graph of y=f(x)
•The real zeros of the function f
•The real solutions to the equation f(x)=0
Use the equation f(x)=4x−28 to verify that all three do produce answers that are numerically the same.
Huh?
The three questions are all the same. Of course they all have the same answer.
0 = 4 x - 28
x = 28/4
x = 7
To find the x-intercepts of a graph, we need to solve the equation f(x) = 0. In this case, the equation is f(x) = 4x - 28. To find the x-intercepts, we set f(x) equal to 0:
4x - 28 = 0
Now, we can solve for x. Adding 28 to both sides of the equation:
4x = 28
Dividing both sides of the equation by 4:
x = 7
So, the x-intercept of the graph occurs at x = 7.
To find the real zeros of the function f, we need to solve the equation f(x) = 0. In this case, the equation is f(x) = 4x - 28. We already solved this equation to find the x-intercept, and we found that x = 7. This means that the real zero of the function f is x = 7.
Lastly, to find the real solutions to the equation f(x) = 0, we also follow the same process. Again, the equation is:
4x - 28 = 0.
Solving for x, we get:
4x = 28
Dividing both sides by 4, we find:
x = 7
So, the real solution to the equation f(x) = 0 is x = 7.
To verify that all three answers are numerically the same, we can see that for the equation f(x) = 4x - 28, the x-intercept is x = 7, the real zero is x = 7, and the real solution to the equation f(x) = 0 is also x = 7. Thus, all three answers are numerically the same.