Question

Given the graph of y = f (x), sketch the graph of the transformation y= -f(1/2 x) + 3

Answer 1

sketch the transformation of the graph

Answer 2

or let me know how it is suppose to look

Answer 3

first take f(x/2). By this transformation the graph will be stretched along x axis (around y axis) . So the x - intersection points will be 0 and -6 ( when x=0 you get f(0/2)=0 and when x=-6 you get f(-6/2)=f(-3) which is 0 ).

then take -f(x/2). By this you'll have to mirror the graph around x axis.

finally to get -f(x/2)+3 you have to shift the graph up along the y axis 3 units.

Answer 4

where did you get -6 from? its suppose to be -3/2

Answer 5

i'm trying to sketch the graph but I'm having some problems. after the entire process, what are all the coordinate suppose to be?

Answer 6

I was referring to the point where the function is equal to 0. So the f is 0 at x=0 and x=-3. i.e. f(0) and f(-3). So when the function is f(x/2), for the function to become f(-3) x has to be -6 so the f(x/2) =f(6/2)=f(3)

By coordinates, if you mean the points where the graph meets the x axis, that we cannot tell exactly. You can refer to the image that i've attached above

Answer 7

ok. i seee that. but the problem i'm having is how the graph looks when translated 3 units up on the y-axis

Answer 8

oh i got it. thank you very much

Answer 9

You're welcom :)

Answer 10

can you help me with one last problem?

Answer 11

Solve each inequality graphically. State the solution and graph the solution: