Can someone help me I don’t know how to do this it’s hard and confusing me
1 answer:
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Answer:
- increasing on 0 < x < 2
- f(2) = 4
- decreasing on 2 < x < 5
Step-by-step explanation:
You need to know that an even function is symmetrical about the y-axis. The graph to the right of the y-axis is the mirror image of the graph to the left. With that in mind, the questions are easily answered.
It might help to draw the function graph, as we did in the attached. Then it is more straightforward to see what is happening in each of the intervals.
The function is increasing in the interval 0 < x < 2.
The function value at x=2 is 4: f(2) = 4.
The function is decreasing in the interval 2 < x < 5.
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(PART-A): s-intercept in this case represents the y-intercept of the graph, whereas the t-intercept in this case represents the x-intercept of the graph.
Always remember that y-intercept represents the value of y where the curve (or line) crosses the y-axis, and x-intercept represents the value of x where the curve (or line) crosses the x-axis.
In the graph attached with the question, at point (0,6) the curve crosses the y-axis. Therefore, the <em>y-intercept (s-intercept) in this case is 6</em>. It means that in year 2000 (t=0), 6 hundred shirts were sold.
However, there is no point on the graph where the curve crosses the x-axis, meaning there is <em>no x-intercept (t-intercept)</em>. It means that there is <em>not</em> a single year when the number of shirts sold is 0.
(PART B): As you can see in the graph (attached with the question) that the <em>f(t)</em> is increasing (exponentially) with the increase in <em>t. </em>Therefore, we can safely say that as t increases without bound, the f(t) increases (also). In this context, it means that the sale of shirts increases as the years go by. Hence, the correct blank is "increases."
(PART C): The average rate of change is actually the slope. To find the slope, we can use the following formula:
slope = --- (X)
Given points: (5, 12.5) and (7, 22). Plug the values in equation (X),
slope =
Hence, the average rate of change for the function between t=5 and t=7 is 4.75 (answer).
(PART D): This part is bit tricky. Therefore, read the explanation carefully!
You can see in the graph that number of Shirts sold is in <em>hundreds. </em>It means that 1 unit (of y-axis in a graph) represents 100 shirts. Therefore, as in the question it is mentioned that there are 1000 T-shirts sold, it will become 10 units (since 10*100 = 1000). So, the function g(t) will become the following:
--- (Y)
Why did I add f(t)? Because in the question, the word "<em>and</em>" is underlined. It means that g(t) represents not only 1000 T-shirts (10*100 = 1000) sold at the basketball games each year, but it also has the number of T-shirts sold ONLINE, which is f(t).
Now insert f(t) in (Y) and solve:
Hence, g(t) is