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Answer:</h2><h3>
A. Domain </h3>
The domain of a function is the x-values that the graph applies to. This means that the domain is whatever x-values the graph crosses. All vertical parabolas (like the one pictured) have a domain of all reals. This is because any x-value could be plugged into the function and provide a y-value. while it may not seem like it, that graph will cover every single x-value in existence.
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B. Range</h3>
The range is similar to the domain but is for y-values. So, the range is whatever y-values the graph applies to and crosses. As you can see from the graph, there are no y-values above 1. This means the range is y≤1.
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C. Increasing Interval</h3>
A graph is increasing when the y-values are increasing. So, on the parent function of a parabola, the graph increases to the right and decreases to the left. However, this graph is inverted and shifted to the left, so the interval will also be flipped and shifted. In this case, the graph increases from -∞ to 2.
- Increasing Interval = [-∞, 2]
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D. Decreasing Interval</h3>
The decreasing interval is very similar to the increasing interval. This interval applies when the y-values are decreasing as the x-values increase. For a parabola, the increasing and decreasing intervals always meet at the x-value of the vertex, which is 2 on this graph. The y-values decrease during the interval 2 to ∞.
- Decreasing Interval = [2, ∞]
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E. Opening</h3>
The direction of a parabola is decided by the sign (+ or -) of the leading coefficient. Positive coefficients open up and negative opens down. As you can see from the graph, the sides of the parabola point downwards. This means that the leading coefficient must be negative.
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F. Min and Max</h3>
A parabola will always only have a min or a max, never both. If a graph opens up it has a min because there is one y-value which is the minimum possible y-value. Graphs that open downwards have a maximum because there is one y-value that is the largest possible. So, this graph has a maximum of 1 because that is the largest possible y-value.
90 words in 4 minutes is the same as 45 words in 2 minutes because you divide both sides by 2. 2 goes into 10, 5 times, so 45x5=225.
You can expect her to type 225 words in 10 minutes.
That would mean it would be 10:25
Answer:
It took Markus half an hour to drive home from work. He averaged 34 miles per hour. How far does Markus live from his work?
Solution
We are given that it takes 1/2 an hour for the trip. This is a time:
t = 1/2
We are given that he averages 34 miles per hour. This is a rate:
r = 34
We are asked how few he has traveled. This is a distance. We use the d=rt equation:
d = rt
= (34)(1/2)
= 17
Markus lives 17 miles from work.
Now try one by yourself. If you want to see the answer, put your mouse on the yellow rectangle and the answer will appear.
Exercise 1
The current along the beach is moving towards the south at 1.5 miles per hour. If a piece of debris is placed into the water, how far will the current take it in 6 hours?
Step-by-step explanation:
