Jacob is incorrect. The transformation was no a reflection, but a translation. The transation was (x+11,y+6)(11 units rigth and 6 units up). (Explain what the points would have been if it was a reflection across the x-axis)
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: 31 hope this helped
Step-by-step explanation: I'm assuming your problem looks like this: 4+5*6-3 =? To solve this problem you need to use the order of operations. PEMDAS which stands for Parentheses, exponents, multiply and divide, and lastly add and subtract. You must multiply and divide before you add and subtract so you must do 5*6 first. You now get 4+30-3. Now all you have left is addition and subtraction so you now just go from right to left and do one at a time. So 4+30 = 34 , 34-3=31. Therefore your answer should be 31. Hope that helped!
(1) For the parabola on the bottom row, the domain would be R and the range would be y ≥ -5
(2) For the hyperbola on the bottom row, the domain would be R\{3} (since there is an asymptote at x = 3) and the range would be R\{4} (since there is an asymptote at y = 4)
(3) For the square root function on the bottom row, the domain would be x ≥ -5 and the range would be (-∞, -2]
(4) For the function to the very right on the bottom row, the domain would be R and the range would be (-∞, -3]
Answer:
2 solutions; x=2.5 x=-25
Step-by-step explanation:
16x^2 = 100
x^2 = 100/16
x^2 = 6.25
x = (+-) sqrt 6.25
x = (+-) 2.5
