Question

Hello I'm stuck with these two questions

The point (1,-2) is on the graph of . Describe the following transformations on , and determine the resulting point.

a) g(x)=f(x+1)-3

b) -f(2x)

Answer 1

to shift the graph of f(x) right by h and up by k,

y-k = f(x-h)

So, g(x) can be written

g+3 = f(x+1)

so, it is the graph of f shifted left 1 and down 3

-f(x) is f(x) reflected in the x-axis, since the sign of y changes.
f(2x) is the graph of f shrunk horizontally by a factor of 2, since 2x changes twice as fast as x. Everything shows up half as far away.

-f(x) is f(x)
reflected in the x-axis and shrunk horizontally by a factor of 2. Or, if you will, dilated by 1/2.

Answer 2

is the new point for a) (1,1)