# Thread: modulus functions and trasformations of graphs

1. ## modulus functions and trasformations of graphs

hey im stuck on this question

The graph of y=|2x-4| + k touches line y=x at only one point. find values of constant k

thanks

2. Originally Posted by elliegurl
hey im stuck on this question

The graph of y=|2x-4| + k touches line y=x at only one point. find values of constant k

thanks
HI

$[|2x-4|+k]^2=[x]^2$

$(2x-4)^2+2(2x-4)(k)+k^2=x^2$

$3x^2+(4k-16)x+k^2-8k+16=0$

b^2-4ac=0 because it touches only at one point .

Solve

$
(4k-16)^2-4(3)(k^2-8k+16)=0
$

3. thankyou so much

i do have another questions about real roots that im stuck on too

show f(x)=4 has no real roots.. f(x)=3-|2x-1|

i've ended up with a eq of -|2x-1|=1 is that right if it is what do i do next lol

4. Originally Posted by elliegurl
thankyou so much

i do have another questions about real roots that im stuck on too

show f(x)=4 has no real roots.. f(x)=3-|2x-1|

i've ended up with a eq of -|2x-1|=1 is that right if it is what do i do next lol
$4=3-|2x-1|$

$1=-|2x-1|$

Similar to your pervious question , square both sides to get rid of the modulus , then use $b^2-4ac<0$ since it has NO real roots . Give it a try !