Question

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?

Answer 1

Option (C).

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.