Help on functions problem?

First remember that always work with the left/right (x axis) direction and then the up/down (y axis) one/

now if f(x) = x^4 and we suppose x= a

then f(a) = a^4

now if we move this 4 units to the left it means that for x= a-4 the value of f(x) is STILL a^4, because the graph only moves horizontally.

x =a-4

a=x+4

substitute in f(x+4) = (x+4)^2

now we have to move 3 down which is the easy part since the y intercept also moves down

now suppose x= b and then f(b) = b^4

but if we are moving 3 steps down then for x= b f(b) = b^4 -3

so final function is y = (x+4)^2 -3

For your second problem

the function after moving 6 steps right means that now f(x) = (x-6)^4

stretching vertically by 2 means that for some x= b if f(b) was (b-6)^4, now it is 2(b-6)^4

so the function is now f(x) = 2(x-6)^4

and FINALLY

reflecting in y axis means that if for x = c, f(c) was (c-6)^4 , now it is (-c-4)^4

i.e f(x) = 2(-x-6)^4

HOPE THAT HELPS

For the first one, the downward shift is reflected correctly by the -3. The left shift, however needs to be (x + 4)^4, not (x^4 + 4).

Make that change, and you're good to go. Same thing for the right shift on the second; (x - 6)^4.

f(x) = x^4; shift downward 3 units and shift 4 units to the left

g(x) = (x + 4)^4 - 3........................................Ans

Note when shifting downward then - units or when shifting up + units

when shifting to the left then add in x or subtract from x for the right

2. f(x) = x^4; shift right 6 units, stretch vertically by a factor of 2, and reflect about the y-axis

g(x) = 2(- x - 6)^4..........................Ans

If -3 is an x-intercept, then the function has (x+3) as a ingredient (plugging x=-3 will provide f(-3)=0). yet another ingredient is (x-a million) for our different intercept x=a million. Multiplying those 2 factors provides a coefficient of a million for x² so which you may double it to get a=2. answer: f(x) = 2(x+3)(x-a million) = 2x² + 4x - 6.

Shifting left or right is done by adding or subtracting from x. Shifting up or down is done by adding or subtracting from f(x). Stretching or compressing is done by multiplying or dividing f(x) by the scaling factor. Reflecting around the y axis is done by replacing x with (-x). Reflecting around the x axis would be done by replacing f(x) with -(f(x)).

Your errors are centered around the left-right shifting. To shift the function to the left, you would want to replace each instance of x with (x-c), where c is the amount of the shift. To shift to the right, replace each instance of x with (x+c).

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