Edward surveyed his friends about whether or not they go to the movies and whether or not they go to professional soccer games.
He reported the relative frequencies in the table. Which statement is correct?
A) Very few of his friends go to professional soccer games.
B) Very few of his friends go to the movies and go to professional soccer games.
C) The majority of his friends go to professional soccer games and go to the movies.
D) He has a lot of friends that do not go to the movies and do not go to professional soccer games
A) Very few of his friends go to professional soccer games.
B) Very few of his friends go to the movies and go to professional soccer games.
C) The majority of his friends go to professional soccer games and go to the movies.
D) He has a lot of friends that do not go to the movies and do not go to professional soccer games
2 answers:
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Answer:
- g(20) > f(20)
- g(x) exceeds f(x) for any x > 4
Step-by-step explanation:
As with most graphing problems not involving straight lines, it works well to start with a table of values. Pick a few values of x and compute f(x) and g(x) for those values. Plot the points and draw a smooth curve through them.
As in the attached, your table will show that there are two points of intersection between f(x) and g(x), and that for values of x more than 4, g(x) becomes much greater very quickly. Both curves rapidly reach the top of your graph space.
To find whether f(20) or g(20) is greater, you can evaluate the functions for that value of x.
f(20) = 20² = 400
g(20) = 2²⁰ = 1,048,576
Clearly, g(20) has a greater value.
