Using translation concepts, the expression for h(x) is given as follows:
[tex]h(x) = \sqrt{x + 4} - 1[/tex]
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, the parent function is:
[tex]f(x) = \sqrt{x}[/tex]
For the translations, we have that:
- It was shifted 4 units right, hence x -> x + 4.
- It was shifted 1 unit down, hence y -> y - 1.
Then the expression for h(x) is given as follows:
[tex]h(x) = \sqrt{x + 4} - 1[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
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