So I need some help on these Graphing Square Root Functions Quiz questions.
1. Simplify 2 over √5
2. Simplify -11√112
3. Simplify 17√17-9√17
4. simplify 6 over √3 + 2
5. what is the domain of the function y=3√6x+42
6. What are the domain and range of the function y=2√3x+4-5
7. Which of the following is a graph of the equation y= √x-5-2
8. Which function is shown on the graph below?
As an AI language model, I cannot provide a visual representation of the graph or images. Please provide more information or context for me to assist you better.
Sure, I can help you with these graphing square root functions questions. Let's go through each question step-by-step:
1. Simplify 2/√5:
To simplify this, we need to rationalize the denominator. To do this, we multiply both the numerator and denominator by √5.
So, (2/√5) × (√5/√5) = (2√5)/5. Therefore, the simplified form is (2√5)/5.
2. Simplify -11√112:
To simplify this, we need to factorize 112 and simplify any perfect square factors under the square root.
112 can be factored as 16 * 7. So, -11√112 can be written as -11√(16 * 7).
The square root of 16 is 4. So, -11√(16 * 7) = -11 * 4√7 = -44√7.
3. Simplify 17√17-9√17:
Both terms have a common factor of √17. So, we can factor that out.
17√17 - 9√17 = √17(17 - 9) = √17 * 8 = 8√17.
4. Simplify 6/√3 + 2:
To simplify this, we need to rationalize the denominator. Multiply both numerator and denominator by √3.
So, (6/√3 + 2) × (√3/√3) = (6√3 + 2√3√3) / (√3√3) = (6√3 + 2√3√3) / 3.
Simplifying the denominator gives us (6√3 + 2√3√3) / 3 = (6√3 + 2√3 * 3) / 3 = (6√3 + 6√3) / 3 = (12√3) / 3 = 4√3.
5. The domain of the function y = 3√(6x) + 42:
Since the function is a square root function, the expression under the square root should be non-negative (≥ 0). So, 6x ≥ 0. Solving this inequality gives us x ≥ 0. Therefore, the domain of the function is all real numbers greater than or equal to zero (x ≥ 0).
6. The domain and range of the function y = 2√(3x) + 4 - 5:
To find the domain, we need to consider the expression under the square root. For the expression to be non-negative, we need 3x ≥ 0. Solving this inequality gives us x ≥ 0. Therefore, the domain is all real numbers greater than or equal to zero (x ≥ 0).
The range of the function can be found by considering the minimum value of the square root function. Since the square root function always gives non-negative values, the minimum value for y is 0. Therefore, the range of the function is y ≥ 0.
7. Since there is no graph provided in the question, it's not possible to determine which graph is the correct one for the equation y = √x - 5 - 2.
8. Without a graph provided, it is not possible to determine which function is shown on the graph.