How does the graph of g(x) = (x − 2)3 + 6 compare to the parent function of f(x) = x3?
1 answer:
The graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.
<h3>How does the graph of g(x) compare to the one of f(x)?</h3>
Here we have:
You can notice that if we take f(x), and we shift it 2 units to the right, we have:
g(x) = f(x - 2)
Then if we apply a shift upwards of 6 units, then we have:
g(x) = f(x - 2) + 3
Replacing f(x) by the cubic parent function, we have:
So we conclude that the graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.
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<h2>Answer:</h2>
The equation that is used to model the length of ladder in terms of x is:
We can model this problem with the help of a right angled triangle whose hypotenuse is 13 meters and the other two legs are x meters and (x-7) meters.
where x is the distance between the top of the ladder and the ground.
and (x-7) is the distance between the foot of the ladder and the wall.
Hence, using Pythagorean Theorem we have:
Hence, the answer is: