Given f(x)=x^2, after performing the following transformations:shift upward 26 units and shift 45 units to the right, the new function g(x)=

Answer 1

To solve this problem it is first helpful to understand transformations of functions in general.

Given a f( bx - c ) + d, where a, b, c, and d are constants, the transformation types are the following:

a: vertical stretch/compression (compression if 0 < |a| < 1 or stretch if |a| > 1)

b: horizontal stretch/compression (stretch if 0 < |b| < 1 or compression if |b| > 1)

c: horizontal translation (right if c is positive or left if c is negative)

d: vertical translation (up if d is positive or down if d is negative)

Also note that if a is negative there is a reflection about the x-axis and if b is negative there is a reflection about the y-axis.

Now using this we can see that if f(x) = x² and the transformation is 26 units up and 45 units right, then g(x) = (x - 45)² + 26.