Question

Given that
$f(x) = {x}^{2}$
Type a function that would shift f(x) right 2.5 units, down 7 units, vertically shrink the function by a factor of 2/5, and reflect is across the x-axis.

Answer 1

f(x) = x^2

shift f(x) right 2.5 units means x becomes x+2.5

so now f(x) = (x+2.5)^2

shift f(x) down by 7 units means f(x) -7

so now f(x) = (x+2.5)^2 - 7

vertically shrink the function by a factor of 2/5 means multiplying f(x) by 2/5

so now f(x) = 2/5[(x+2.5)^2-7]

reflect across the x-axis means f(x) becomes -f(x)

so now f(x)=-2/5[(x+2.5)^2-7]

f(x) = (-2/5)x^2 - 2x + 3/10

Answer 2

f(x) = x^2

1st transpose f(x) = (x+2.5)^2

2nd transpose f(x) = (x+2.5)^2 - 7

3rd contract f(x) = 2/5*((x+2.5)^2-7)

4th reflect f(x) = (-2/5)((x+2.5)^2-7)

f(x) = -0.4x^2 - 2x + 0.3