Question

Select all the transformations of f(x) = x2 that combine to result in the graph of

function g below.
ny
2
х
14
-2
0
4
2
4
6
translation of 2 units up
horizontal stretch by a factor of 2
translation of 1 unit left
reflection across the x-axis

Answer 1

Explain below

Explanation:

I wonder if you listed the complete set of options? The transformation from f(x) to the graph shown (name it as g(x)) should be..

f(x) = x²

g(x) = -1/4 (x+1)² - 2 .. calculate through vertex (h,k) = (-1,-2) and y = a(x-h)²+k

1. 1/4: vertical compression of factor 1/4

2. negative: f(x) -> -f(x): reflection over x axis

2. x -> x+1 f(x) -> f(x+1): horizontal translation left 1 unit

3. -2: vertical translation DOWN 2 units