Let f(x) = 4|x|
1 answer:
Answer:
g(x)=4|x-5|
Step-by-step explanation:
Since the question wants you to <em>shift 5 units to the right</em>, all you need to do is add that - 5 inside the absolute value with the x, and it will shift the function 5 units to the right. I even attached a picture to prove that when adding - 5 inside the absolute value with the x, it shifts the function g(x) 5 units to the right.
Hope this helps! :)
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the function is given, and it's value is where the object is ("how far to the right").
so as long as it rises (going more right), this will be apply.
in the screenshot I graphed the function. of course t is graphed as x and "along the x-axis" is graphed as y, but the pattern is the same anyways.
for the first 1.25 seconds the object goes to the left, and after that always to the right.
since we look at t to calculate x, t effectively takes the role of the important variable that is normally given to x. the calculation pattern are just the same. so let's find the lowest point of this function by calculating it out.
x(t) = 2t² – 5t – 18
x'(t) = 4t -5
x'(t) = 0
0 = 4t -5
5 = 4t
1.25 = t
plugging it into the second derivative
x''(t) = 4
x''(1.25) = 4
it's positive, so at t=1.25 there is a low point
(of course the second derivative is constant anyways.)
the object is traveling toward the right
the object is traveling toward the rightfor t > 1.25
