Question

how can you tell if a graph is invertible just from the equation given? Examples: x^6+x3+1, e^x^(2-1)

Answer 1

invertible means?

Answer 2

reflection across what axis?

Answer 3

invertible is when none of the y coordinates repeat

Answer 4

so y axis?

Answer 5

\(x^6\) is a clue that it is not

Answer 6

so if any exponents in the function are even, then it is not invertible?

Answer 7

the function is not even, but the degree is

Answer 8

that means the "end behaviour" as i now see it called is it starts from top left and ends at top right, so it will not pass the "horizontal line test"

Answer 9

oh i see

Answer 10

as for the second one, i have no idea what
\[e^{x^{2-1}}\] means

Answer 11

Is there a way to tell just by looking at the equation without graphing or plugging in points?

Answer 12

sure, i just told you without a picture
my picture was fiction, a mental picture