If fx squareroot x 1 and gx 3fx 3 7 state in words the

If f(x) = squareroot x + 1 and g(x) = 3f(x - 3) + 7 state in words the transformation to go from f(x) to g(x) If h(x) = 1/2 f(5x) - 4, what are the steps from f(x)?

Solution

f(x) = sqrt(x+1) ; g(x) = -5 f(x -3) +7

Following transformations are applied:

i) Shift horizontally to right by 3 units : f(x-3)

ii) Stretch in the y dierection by multiplying a f actor 5 : 5f(x-3)

iii) Refelct acroxx x axis: -5f(x -3)

iv) Vertically shift up by 7 units : -5f(x -3) +7

h(x) = (1/2)f(5x) -4

Following transformations are applied:

i) stretch it in the x-direction by multiplying x by a factor 5

ii) compress it in the y-direction by multiplying the whole function by a (1/2) : (1/2)f(5x)

iii) Shift vertically down by 4 units : . (1/2)f(5x) -4