Question

let g be a horizontal shrink by a factor of 1/3 followed by a translation 2 units up and 4 units left of the graph f(x)=3x-2)^2+5

Answer 1

To find the equation of g, we need to apply the transformations to the equation of f. The equation of f is:

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

A horizontal shrink by a factor of 1/3 means that we need to divide x by 1/3, or equivalently, multiply x by 3. This gives us:

f(3x) = (3(3x) - 2)^2 + 5 f(3x) = (9x - 2)^2 + 5

A translation 2 units up and 4 units left means that we need to add 2 to the y-value and subtract 4 from the x-value. This gives us:

g(x) = f(3(x + 4)) + 2 g(x) = ((9(x + 4) - 2)^2 + 5) + 2 g(x) = (9x + 34)^2 + 7

Therefore, the equation of g is:

g(x) = (9x + 34)^2 + 7