Question

Let f(x) = sqrt(x)
a. Find a formula for a function g(x) whose graph is obtained from the graph of f by reflecting across the x-axis, then shifting 2 units up and 4 units to the left.
b) Find a formula for a function h(x) whose graph is obtained from f by first shifting 2 units up and 4 units to the right, then reflecting across the x-axis

Answer 1

I think the first one is g(x) = sqrt(-x+4) + 2

Answer 2

g(x) = -sqrt(x+4) + 2 ?

Answer 3

sorry g(x) = -sqrt(x-4) + 2

Answer 4

If it is on the outside, then it is reflected across the y-axis and on the inside across the x-axis if I remember it right

Answer 5

you are right in your 1º answer

Answer 6

can't get it to graph on the calculator with it reflected

Answer 7

For part b, I have h(x) = -sqrt(x-4) + 2

Answer 8

first y = sqrt(x) is only valid for x>=0
on reflection with x axis y becomes negative
so y = - sqrt(x)
then you shift it two units up
y = - sqrt(x) + 2
then shift it 4 left so y = - sqrt(x+4) + 2

for second part y = - sqrt(x-4) -2

Answer 9

so for the first one, is the - inside of the radical and on the second part outside of it?

Answer 10

@iambatman

Answer 11

so my answers for part a and b are
g(x) = sqrt(-x+4)+2
h(x) = -(sqrt(x-4))+2

Answer 12

Look lets start with example if for y = sqrt(x), x=4 then on reflection value of y is inverted, like if initially y=2 for x=4 now y is -2, now if you shift it up then 2 gets added
y= - sqrt(x) + 2, shifting left means y = -sqrt(x+4) + 2
eg point (16,4) reflected = (16, -4), displaced upwards (16, -2) displaced left (12, -2)
satisfies equation y = -sqrt(x+4) +2

Similarly proceed for the second case

Answer 13

I remember if you shift left, it is positive and if you shift right it is negative

Answer 14

what do you mean by displaced upwards and displaced left?