Vertical & horizontal shifts

Question

can you help me solve this problem:

Use the technique of Stretching, Shrinking and Reflection to graph the following function.

𝑦 = −√1 − 𝑥

a. What is the parent function?

b. Are there any Vertical Compression, Expansion, or reflections? If so, please state

them accordingly.

c. Are there any Horizontal Compression, Expansion, or reflections? If so, please

state them accordingly.

d. Graph

i know that the parent function is y=square root x. However I’m having trouble understanding how to know if it compresses, stretches, or reflects. And if it reflects, over which axis? Also, when I graph the parent function would I use the range values of 4,9,16 and plug in to find y?

Answer 1

b) y = - √(1-x) = -1√(1-x)

The magnitude of -1 is 1 means no expansion or compression.

The sign is negative means reflection about the x-axis

c) (1 - x) = -1(x-1) we have no horizontal compression or expansion but reflection about the y axis

As we have (x - 1), this means we move 1 to the right.

d) If you follow step c, this would tell you how to figure out the values of x to use in the plot.

Reflecting about the y axis, we want x = 0, -1, -4, -9, -16. Moving one to the right (adding 1), we have 1, 0, -3, -8, -15

If you plug in these values to y = - sqrt(1 - x), you get what you want.

-sqrt(1 - 1) = 0, - sqrt(1 - 0) = -1, -sqrt(1 - -3) = -2, -sqrt(1 - -8) = -3, -sqrt(1 - -15) = -4

We have (1, 0), (0, -1), (-3, -2), (-8, -3), (-15, -4)