can someone check my work for this question?
the question is to graph the function of square root of x plus 2 with the plus 2 not being in the square root
my x values were 0,1, 4, 9, and 16
my y values were 2, 3, 4, 5, and 6
the next part says to write the domain and range. for domain I had x> or equal to 0. for the range I had y> or equal to 2
thank you for checking my work!
all correct
You can write >= for "greater than or equal"
same for <=
as intervals, the domain and range are
x∊[0,∞)
and
y∊[2,∞)
To graph the function f(x) = √(x + 2), you have correctly chosen the x-values as 0, 1, 4, 9, and 16.
Now let's calculate the corresponding y-values:
For x = 0, f(0) = √(0 + 2) = √2 ≈ 1.414
For x = 1, f(1) = √(1 + 2) = √3 ≈ 1.732
For x = 4, f(4) = √(4 + 2) = √6 ≈ 2.449
For x = 9, f(9) = √(9 + 2) = √11 ≈ 3.317
For x = 16, f(16) = √(16 + 2) = √18 ≈ 4.243
So, the corrected y-values for the given x-values are approximately 1.414, 1.732, 2.449, 3.317, and 4.243.
Regarding the domain and range:
The domain of the function represents all possible x-values for which the function is defined. In this case, since the function is a square root, the expression inside the square root must be non-negative. Therefore, the domain is x ≥ -2. So, your domain statement of x ≥ 0 is not entirely correct. It should be x ≥ -2.
The range of the function represents all possible y-values that the function can take. Since the square root function always gives non-negative outputs, the range is y ≥ 0. Therefore, your range statement of y ≥ 2 is not entirely correct. It should be y ≥ 0.
So, to summarize:
Domain: x ≥ -2
Range: y ≥ 0
To graph the function of square root of x plus 2, where the "+2" is not inside the square root, you have correctly chosen some x values and evaluated the corresponding y values. The x values you selected are 0, 1, 4, 9, and 16. The y values you calculated for each x value are 2, 3, 4, 5, and 6, respectively.
Next, to write the domain and range of the function:
1. Domain: The domain represents all the possible x values. In this case, the square root of x plus 2 is defined for any non-negative real numbers since x cannot be negative for square roots. Therefore, the domain is x ≥ 0, as you correctly stated.
2. Range: The range represents all the possible y values. By evaluating the function for the selected x values, you have determined that the y values range from 2 to 6. Hence, the range is y ≥ 2, as you correctly stated.
In summary, it appears that you have correctly graphed the function and determined the domain and range. However, without actually seeing the graph itself, I cannot verify its accuracy visually.