how many zeros are indicated by the values in the table that represent the graph of a continuous…
how many zeros are indicated by the values in the table that represent the graph of a continuous function?\n| x | y |\n| -3.0 | 8.40 |\n| -2.4 | 0.69 |\n| -1.8 | -0.39 |\n| -1.2 | 0.24 |\n| -0.6 | 0.46 |\n| 0 | 0 |\n| 0.6 | -0.46 |\n| 1.2 | -0.24 |\n| 1.8 | 0.39 |\n| 2.4 | -0.69 |\n| 3.0 | -8.40 |\n3\n4\n5
Answer
Explanation:
Step1: Recall zero - value definition
A zero of a function is a value of $x$ for which $y = 0$.
Step2: Check table values
We look at the $y$-values in the table. When $x = 0$, $y=0$. Also, since the function is continuous, and the sign of $y$ changes (from positive to negative or vice - versa) between $x=-2.4$ and $x = - 1.8$ and between $x = 0.6$ and $x=1.2$, by the Intermediate Value Theorem, there must be a zero in each of those intervals.
Answer:
3