Question

Describe the transformations:

f(x) = 2(x-4)²-1
stretch by 2, left 4, down 1
stretch by 2, right 4, down 1
stretch by 2, right 3, down 1
O right 8, down 1

Answer 1

stretch by 2, right 4, down 1

Explanation:

In a function in the form:

f(x) = a(x - h)² + k

the number in front, a, shows vertical stretch (if its bigger than 1. Its a shrink or smash if its a fraction less than 1)

Horizontal shifts are shown in close next to the x, inside the parenthesis shown here with an h. Horizontals shifts are maybe the opposite of what you might think they should be. + anumber is a left shift and - anumber is a right shift.

Vertical shifts are shown by a number tacked onto the end of the equation, k These shifts are more intuitive. + anumber shifts up and - anumber shifts down.

For your equation:

f(x) = 2(x-4)²-1

The 2 is a vertical stretch. The -4 by the x is a right shift 4. The -1 tacked into the end is a shift down 1