Help please and thank you: The graph of f x = x2 − 2x − 3 is shown. Which of these describes the effect changing f x to f −2x will have on the graph?

Option (C).

Step-by-step explanation:

Graphed function is,

f(x) = x² - 2x - 3

     = x² - 2x + 1 - 1 - 3

     = (x² - 2x + 1) - 4

     = (x - 1)² - 4

f(-2x) = (-2x)² - 2(-2x) - 3

        = 4x² + 4x - 3

        = 4(x² + x) - 3

        = 4[x² + 2(0.5)x + (0.5)²- (0.5)²] -3

        = 4(x + 0.5)² - 1 - 3

        = 4(x + 0.5)² - 4

        = 4[(x - 1) + 1.5]² - 4

Therefore, parent function 'f' will be a horizontal shrink by 4 units and  shifted 1.5 units to the left.

Option (C) will be the answer.

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

191 students play sports and ninety-seven 10th graders were surveyed.

step-by-step explanation: