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  1. Home
  2. 12th grade
  3. Calculus
  4. Exercise : Use the intermediate value theorem to make statements about a function

Use the intermediate value theorem to make statements about a function Calculus

Here are some values of a function f, that is known to be continuous.

x f(x)
-2 2
1 -1
3 -1
4 5

Statement: "f has exactly one x-intercept".

Here are some values of a function f, that is known to be continuous.

x f(x)
2 -2
3 -2
4 1
5 -4
6 -3
7 5

Statement: "f has at least two x-intercepts on the domain 3 \leq x \leq 5 "

Here are some values of a function f, that is known to be continuous.

x f(x)
-1 1
0 1
1 -1
4

7

6 7
7 -2

Statement: "f has exactly two x-intercept".

Here are some values of a function f, that is known to be continuous.

x f(x)
-3 9
0 7
2 9
5 -4
6 -3
8 -4

Statement: "f has at least one x-intercept."

Here are some values of a function f, that is known to be continuous.

x f(x)
-1 1
1 -1
3 3
5 4
8 3
13 2
14 -2

Statement: "f has no more than two x-intercepts."

Here are some values of a function f, that is known to be continuous.

x f(x)
-3 -4
3 -2
4 2
5 8
8 -2

Statement: "f has no x-intercepts on the domain -3 \leq x \leq 4. "

Here are some values of a function f, that is known to be continuous.

x f(x)
-10 4
-4 -2
-3 -2
-1 -5
4 3
5 3
7 6

Statement: "f has less than two x-intercepts."

See also
  • Course : Continuity of functions
  • Exercise : Determine the continuity of a piecewise function at a point
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