Standard from 0.000000017
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Answer:
[-3, ∞)
Step-by-step explanation:
There are many ways to find the range but I will use the method I find the easiest.
First, find the derivative of the function.
f(x) = x² - 10x + 22
f'(x) = 2x - 10
Once you find the derivative, set the derivative equal to 0.
2x - 10 = 0
Solve for x.
2x = 10
x = 5
Great, you have the x value but we need the y value. To find it, plug the x value of 5 back into the original equation.
f(x) = x² - 10x + 22
f(5) = 5² - 10(5) + 22
= 25 - 50 +22
= -3
Since the function is that of a parabola, the value of x is the vertex and the y values continue going up to ∞.
This means the range is : [-3, ∞)
Another easy way is just graphing the function and then looking at the range. (I attached a graph of the function below).
Hope this helped!
Answer:
Step-by-step explanation:
The graph that represents the function
f(x) = (x + 4)(x + 1)(x - 3)
crosses the x-axis three times: at x = -4, x = -1, and x = 3
because we apply the zero product rule and found the roots -4, -1, and 3
x+ 4= 0 → x = -4
x+1 = 0 → x = -1
x-3 = 0 → x = 3
