Today's mathematicians would probably agree that the Riemann Hypothesis is the most significant open problem in all of math. It'
1 answer:
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<h2>Hello!</h2>
The answer is:
The first and second options:
f(x) and g(x) intersect at exactly two points.
The x-intercepts of f(x) are common to g(x)
<h2>Why?</h2>To find which of the given options is the correct, we need to remember the following:
- When a function intercepts the x-axis, it means that the "y" coordinate will tend to 0.
- When a function intercepts the y-axis, it means that the "x" coordinate will tend to 0.
So, to find the correct option, we also need to compare the given table to the graphed function.
Now, discarding each of the given options in order to find the correct option, we have:
- First option: True.
f(x) and g(x) intersect at exactly two points.
From the graph we can see that f(x) intercepts the x-axis at two points (-1,0) and (1,0), also, from the table we can see that g(x) intercepts the x-axis at the same two points (-1,0) and (1,0), it means that the functions intersect at exactly two points.
Hence, f(x) and g(x) intersect at exactly two points.
- Second option: True.
The x-intercepts of f(x) are common to g(x)
From the graph we can see that f(x) intercepts the x-axis at two points (-1,0) and (1,0), also, from the table we can see that g(x) intercepts the x-axis at the same two points (-1,0) and (1,0), so, both functions intercepts the x-axis at common points.
Hence, the x-intercepts of f(x) are common to g(x)
- Third option: False.
From the graph, we can see that the minimum value of f(x) is located at the point (0,-1), also, from the given table for g(x) we can see that there are values below the point (2,-3), meaning that the minimum value of f(x) is NOT less than the minimum value of g(x).
Hence, the minimum value of f(x) is NOT less than the minimum value of g(x).
- Fourth option: False:
We can see that for the function f(x) the y-intercept is located at (0,-1) while from the given table, we can see the y-intercept for the function g(x) is located at (0,1)
Hence, f(x) and g(x) have differents y-intercepts.
Therefore, the correct answers are:
The first and second options:
f(x) and g(x) intersect at exactly two points.
The x-intercepts of f(x) are common to g(x)
Have a nice day!
Note: I have attached a picture for better understanding.