Answer:
- Domain [0, infinity)
- Range: [0, infinity)
- x intercept: 0
- y intercept: 0
Step-by-step explanation:
The domain is the set of all allowed input x values. The smallest input we can do is x = 0. Recall that we cannot take the square root of a negative number to get a real number output.
The domain as an inequality is x ≥ 0 which is the same as saying 0 ≤ x < infinity.
Then that condenses to the interval notation [0, infinity)
Use a square bracket to include the endpoint 0. We always use a curved parenthesis for either type of infinity since we cannot reach this (it's not a number to reach).
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The range is the set of possible y outputs. The square root function is always increasing, so the smallest output corresponds to the smallest input.
y = 0 is the smallest output so either y = 0 or y > 0 is possible.
The range as an inequality is y ≥ 0 and leads to the interval notation [0, infinity)
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To find the x intercept, replace f(x) with 0 and solve for x.
f(x) = sqrt(x)
0 = sqrt(x)
x = 0^2
x = 0
It turns out that the x intercept and y intercept are both 0.
Both occur at the origin (0,0)
You can use a graphing tool like GeoGebra or Desmos to confirm these answers are correct.
