Let f be a continuous function on the closed interval [ − 2 , 5 ]. If f((-2)=-7 and f(5)=1, then the Intermediate Value Theorem guarantees that

The function has at least 1 zero within the interval [-2,5].

Step-by-step explanation:

The intermediate value theorem states that, for a function continuous in a certain interval , then the function takes any value between and at some point within that interval.

This theorem has an important consequence:

If a function is continuous in an interval [a,b], and the sign of the function changes at the extreme points of the interval:

(or viceversa)

Then the function f(x) has at least one zero within the interval [a,b].

We can apply the theorem to this case. In fact, here we have a function f(x) continuous within the interval

[-2,5]

And we also know that the function changes sign at the extreme points of the interval:

Therefore, the function has at least 1 zero within the interval [-2,5], so there is at least one point x' within this interval such that

The correct choice is shown selected.

Step-by-step explanation:

Since a radius needs to appear first on the list, it is worthwhile to identify those segments that are radii. A radius extends from the center (O) to a point on the circle. OG and OD are the only ones. The selected answer is the only one that has one of those listed first.

A chord is a line segment whose ends are points on the circle. There are 4 chords in the figure, one of which is also a diameter:

... DG, DH, FG, FH . . . . DG is also a diameter, since it includes the center point, O

There is one tangent: DE, an external line that intersects the circle at one point.