How do you combine this to make a simpler expression?
2 answers:
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<h3>Answer: Choice A</h3>
- Domain: x > 4
- Range: y > 0
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Explanation:
We want to avoid having a negative number under the square root. Solving leads to
So it appears the domain could involve x = 4 itself; however, if we tried that x value, then we'd get a division by zero error.
So in reality, the domain is x > 4.
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The range of y = sqrt(x) is the set of positive real numbers. So y > 0 is the range for this equation. Shifting left and right does not affect the range, so the range of y = sqrt(x-4) is also y > 0.
We are dividing a positive number (3) over some positive number in the denominator. Overall, the expression is positive because positive/positive = positive.
Therefore, the range of the given equation is y > 0
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The graph is shown below. We have a vertical asymptote at x = 4 and a horizontal asymptote at y = 0. The green curve is fenced in the upper right corner (northeast corner).
Answer:
D) y = 1/4 x^2
Step-by-step explanation:
For these functions, the leading coefficient can be considered to be either ...
the vertical scale factor (larger ⇒ narrower)
the square of the inverse of the horizontal scale factor.
In the latter case, the horizontal scale factor will be larger (wider) when its inverse and the square of its inverse are smaller.
Either way, you're looking for the smallest leading coefficient: 1/4.
