Question

How is the graph of the parent function, y = StartRoot x EndRoot transformed to produce the graph of y = StartRoot negative 2 x EndRoot? It is translated horizontally by 2 units and reflected over the x-axis. It is translated horizontally by 2 units and reflected over the y-axis. It is horizontally compressed by a factor of 2 and reflected over the x-axis. It is horizontally compressed by a factor of 2 and reflected over the y-axis.

Answer 1

The graph of the parent function is horizontally compressed by a factor of 2 and reflected over the y-axis ⇒ Last answer

Step-by-step explanation:

Let us revise some transformation

A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis.  

A horizontal stretching is the stretching of the graph away from the y-axis  

• If k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally shrunk (or compressed) by dividing each of its x-coordinates by k.
• If 0 < k < 1 (a fraction), the graph of y = f(k•x) is the graph of f(x) horizontally stretched by dividing each of its x-coordinates by k
• If k should be negative, the horizontal stretch or shrink is followed by a reflection across the y-axis

∵  y = √x is a parent function

∵ Its graph transformed to produce the graph of y = √(-2x)

- That means x is multiplied by a factor k, then it is compressed

   or stretched horizontally

∵ k = -2

- The factor is -2, where 2 is greater than 1, then it is compressed

   horizontally as the first rule above and the negative means

   reflected across the y-axis as the third rule above

∴ The graph of the parent function is compressed horizontally and

    reflected across the y-axis

The graph of the parent function is horizontally compressed by a factor of 2 and reflected over the y-axis

Look to the attached figure for more understand

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Answer 2

Answer:

D on edge

Step-by-step explanation: