tips on drawing inverse functions? (1 Viewer)

[walaili]

not sure how to draw it here and the answer is a

 

[icycledough]

The original function has to be 1-1, thus, they ask you to restrict the domain. The largest domain would be from the vertex onwards, and so when you draw the inverse function, there can only be one intersection point. It's almost a linear equation but with a curve, so it can only intersect each other once.

 

[Siwel]

not sure how to draw it here and the answer is aView attachment 33844

on how to draw it, it depends on what domain you decide on, because you have to be either left of the vertex or right otherwise you fail the horizontal line test. the intersections though all functions and their inverses intersect on y=x, but since only half the parabola is chosen only 1 intersection will be shared between your chosen inverse f(x) and the normal f(x)

 

[walaili]

on how to draw it, it depends on what domain you decide on, because you have to be either left of the vertex or right otherwise you fail the horizontal line test. the intersections though all functions and their inverses intersect on y=x, but since only half the parabola is chosen only 1 intersection will be shared between your chosen inverse f(x) and the normal f(x)

HI, WHAT WOULD THAT LOOK LIKE??
oops sorry caps on, but would my blue line be the inverse

 

[Siwel]

i can show what i came up with but honestly it might be wrong

 

[DheerChoudhury]

HI, WHAT WOULD THAT LOOK LIKE??
oops sorry caps on, but would my blue line be the inverse

You gotta restrict the domain because what you've drawn is a relation. Restrict f(x) to monotonic increasing/decreasing and that will give you your inverse function.

 

[Siwel]

You gotta restrict the domain because what you've drawn is a relation. Restrict f(x) to monotonic increasing/decreasing and that will give you your inverse function.

this correct (the blue line being the inverse)?

 

[DheerChoudhury]

View attachment 33862

this correct (the blue line being the inverse)?

Yeah seems legit

 

[Siwel]

just ignore the fact it intersects twice, just cause when you restrict the domain part of the parabola is disregarded

 

[walaili]

awesome thx guys!! does anyone have tips on drawing inverse functions tho bc i do be flipping my paper in all degrees to sketch

 

[Siwel]

awesome thx guys!! does anyone have tips on drawing inverse functions tho bc i do be flipping my paper in all degrees to sketch

personally for parabolas, I find the vertex, restrict domain to either what they want or my choice (generally to the right of the parabola), then find the restricted range for the parabola given my restricted domain. Flip the domain and range so that they are for the inverse now and then solve for inverse function and plot 3-5 points to understand the general idea then sketch.