Which function would be produced by a horizontal stretch of the graph of y = √ x 𝑦 = 𝑥 followed by a reflection in the x 𝑥 -axis? option 1 of 4 y = √ 2 ( − x ) 𝑦 = 2 ( − 𝑥 ) y = √ 2 ( − x ) 𝑦 = 2 ( − 𝑥 ) option 1 of 4 option 2 of 4 y = − √ 2 x 𝑦 = − 2 𝑥 y = − √ 2 x 𝑦 = − 2 𝑥 option 2 of 4 option 3 of 4 y = √ 1 2 ( − x ) 𝑦 = 1 2 ( − 𝑥 ) y = √ 1 2 ( − x ) 𝑦 = 1 2 ( − 𝑥 ) option 3 of 4 option 4 of 4 y = − √ 1 2 x
Question
Which function would be produced by a horizontal stretch of the graph of y
√ x 𝑦
𝑥 followed by a reflection in the x 𝑥 -axis?
option 1 of 4 y
√ 2 ( − x ) 𝑦
2 ( − 𝑥 )
y
√ 2 ( − x ) 𝑦
2 ( − 𝑥 ) option 1 of 4 option 2 of 4 y
− √ 2 x 𝑦
− 2 𝑥
y
− √ 2 x 𝑦
− 2 𝑥 option 2 of 4 option 3 of 4 y
√ 1 2 ( − x ) 𝑦
1 2 ( − 𝑥 )
y
√ 1 2 ( − x ) 𝑦
1 2 ( − 𝑥 ) option 3 of 4 option 4 of 4 y
− √ 1 2 x
Solution
The correct answer is option 2 of 4: y = -√2x.
Here's why:
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A horizontal stretch of the graph y = √x by a factor of 2 would result in the function y = √(x/2). This is because a horizontal stretch by a factor of 2 means that every x-coordinate in the original function is divided by 2 in the new function.
-
A reflection in the x-axis would then change the sign of the y-coordinate, resulting in the function y = -√(x/2).
-
However, to simplify this function to match one of the given options, we can multiply inside the square root by 2/2 (which is essentially multiplying by 1 and doesn't change the value of the function). This gives us y = -√(2x/4), which simplifies to y = -√2x.
So, the function produced by a horizontal stretch of the graph y = √x followed by a reflection in the x-axis is y = -√2x.
Similar Questions
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