Answer:
s(x) is t(x) ...
- horizontally compressed by a factor of 2,
- reflected across the y-axis, and
- translated downward 5 units.
Domain and Range
- t(x) has a domain of x ≤ 0, and a range of y ≥ 0.
- s(x) has a domain of x ≥ 0, and a range of y ≥ -5.
Step-by-step explanation:
t(x) is the square root function reflected across the y-axis and compressed horizontally by a factor of 2. That is, in f(x) = √x, the x has been replaced by -2x.
s(x) has the function t(x) reflected back across the y-axis and compressed horizontally by another factor of 2. It is also translated downward by 5 units, so that its origin (vertex) is at (0, -5).
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The graph shows you the domain and range of s(x). The domain is all numbers to the right of x=0, including x=0. That is ...
domain: x ≥ 0
The range is all numbers -5 or above:
range: y ≥ -5
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For t(x), the argument of the square root function must not be negative, which means the value of x cannot be positive.
domain: x ≤ 0
For non-negative values of radicand, the t(x) function will have non-negative values. So, the range is ...
range: y ≥ 0
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