Question

The function g(x) has a domain of 0< x< 10 and a range of - 5 < y < 5 . Which of the following sets of points might be on the graph of g(x) ?

Answer 1

We want to see which points could be on the graph of g(x), given that we know its domain and range.

The correct option is d:  (8, 2)

First, for a given function y = f(x) we define the domain as the set of the possible values of x, and the range as the set of the possible values of y.

Here we know that for g(x):

domain: 0 < x < 10

range: -5 < y < 5

So the points (x, y) that could be on the graph of g(x) are these ones where the values of x and y are in the given intervals.

a) (-2, 5)

Here the x-value is x = -2, this is not in the interval (0, 10), so this point can't be on the graph.

b) (-1, 6)

Here the x-value is x = -1, this is not in the interval (0, 10), so this point can't be on the graph.

c) (1, 9)

Here the y-value is 9, it does not belong to the interval (-5, 5), so this point can't be on the graph.

d) (8, 2)

Here both values belong to the correspondent intervals:

x = 8 to (0, 10)

y = 2 to (-5, 5)

So this point can be on the graph of f(x).

Concluding, the correct option is d:  (8, 2)

If you want to learn more, you can read:

https://brainly.com/question/1632425