The given function is a square root function. To draw a graph of this function we will make a table of values using four points.
h(x)=- sqrt(3-x)
Recall that you cannot take the square root of a negative number and obtain the real value. This means that we need to have a non-negative expression under the square root.
3-x ≥ 0We want to know which values of x will give us real solutions.
To do this, we will now isolate the x-variable on one side of the inequality.
As we can see, only the values of x that are less than or equal to 3 will give us real solutions. Thus, the domain of the given function is x ≤ 3 and we should substitute such values into the table to find the points lying on the graph.
x
- sqrt(3-x)
h(x)=- sqrt(3-x)
3
- sqrt(3- 3)
0
2
- sqrt(3- 2)
- 1
- 1
- sqrt(3-( - 1))
- 2
- 6
- sqrt(3-( - 6))
- 3
The ordered pairs ( 3, 0), ( 2, - 1), ( - 1, - 2), and ( - 6, - 3) all lie on the graph of the function. Now we will plot and connect these points with a smooth curve.
Notice that we have already stated that the domain of the given function is all values less than or equal to 3.
Domain:& x ≤ 3
By calculating the value of the function in the maximum value of the domain we can find the maximum value of the range. We already know that h(3)=0. Thus, the range of the given function is all values less than or equal to 0.
Range:& y≤ 0
