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Explanation & Answer
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1. Graph f(x) = √𝑥. Plot at least three points.
x f(x) = √𝒙
0
0
1
1
2
1.41
3
1.73
4
2
5
2.24
6
2.45
a. Use f(x) graph to graph g(x) = √𝑥− 1.
We know that a composition function property is g(x) = f(x) – 1, shift down 1 unit.
b. Use f(x) graph to graph j(x) = √𝑥 − 1
A property of composition function is j(x) = f(x-1), shift right 1 unit.
2. Let f(x) = √𝑥. Use the graph of f(x) from Example 1 to graph the following
functions, also state their domains and ranges.
a. g(x) = √−𝑥.
Let f(x) = √𝑥 then, reflect about y – axis
Hence,
𝑔(𝑥) = √−𝑥
To find the domain we know that a square root cannot have negative values so,
−𝑥 ≥ 0
𝑥≤0
𝑫𝒐𝒎𝒂𝒊𝒏: (−∞, 𝟎]
From the graph the range is,
𝑹𝒂𝒏𝒈𝒆: [𝟎, ∞)
b. j(x) = √3 − 𝑥
Let f(x) = √𝑥 then, reflect about y – axis, shift right 3 units
Hence,
𝑗(𝑥) = √3 − 𝑥
To find the domain we ...
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