hiiii everyone, i really need help with this question please, plz dm me if you can help thanks! :)

[median ibex]

What is your doubt?

[brave smelt]

hii

im just a little confused on ii and iii

[median ibex]

aight

[brave smelt]

i know i is a one to one

but for ii and iii im a little confused

[fast thistle]

bacc

[median ibex]

We recall that an exponential function is a one to one

Now this one has base 9

and was reflected at the y-axis

[brave smelt]

sooo

its a y=a^x graph pretty much right?

[median ibex]

yep

[brave smelt]

so that would not be a one to one

because it passes more than one line

okay

[median ibex]

exponential functions are basically strictly increasing/decreasing

[brave smelt]

makes sense

[median ibex]

so they are also 1 to 1

[brave smelt]

oh

wait im sorry

[median ibex]

Now for (iii) can you draw the piecewise function

[brave smelt]

so ii is a one to one

ohh

but doesnt it fail the hlt

it passes more than one line

[median ibex]

wdym

[brave smelt]

the graph you just drew

[median ibex]

yea what about?

you can see that it would pass the horizontal line test

[brave smelt]

doesnt one to one mean it can only pass one line

[median ibex]

no

one to one means that for each y value there is a unique x value

x^2 for example is not 1 to 1

cause for y = 4 you get x = 2 or x = -2

so not one to one

it also failes the horizontal line test

[brave smelt]

okayy

so i s the only one to one function currently

correct?

[median ibex]

no

(ii) too

[brave smelt]

oh shoot im sorry

im a little rusty lol

ok makes sense

[median ibex]

fr?

[brave smelt]

and you said the piecewise fn of iii

[median ibex]

this is all you have to check

[median ibex]

ye

it's be a linear function for x < 0 which is 1 to 1

now we have to see for the quadratic for non negative

x²+9 is basically x² but 9 units shifted up

so it's only the first half

[brave smelt]

i see now makes sense

[median ibex]

should also be in my head 1 to 1

but still

[brave smelt]

oh okay

[median ibex]

there could be values of the linear function that for the parabola also have x values for

[brave smelt]

so theyre all one to one functions

because i thought at first i and ii were the only one to ones

[median ibex]

ye

But you still need to draw it

like imagine it was x+1 and x²

[brave smelt]

i understand now

but isnt one part of the piecewise fn not one to one

or am i confused

because

[median ibex]

this one failed

[brave smelt]

for x<= -, f(x) =x^2 + 9

[median ibex]

as piecewise

[brave smelt]

i knwo thats quardratic

and therefor thats not a one t one

[median ibex]

you are confused

[median ibex]

If it were here (x-1)²+9 then it wouldn't be 1 to 1 because for y = 10 you get x = 0 or x = 2

but x² is exactly cut half

and so it is strictly increasing

by that passing the horizontal line test

[brave smelt]

which owuld make it aone to one

so that means all of them are one toones

[median ibex]

yes

simple actually

plot them kind of and test

or find a counter example like i did

[brave smelt]

okay i hope its not wrong

okay igot iy right

thanks for the help