Question

The table shows input and output values for a cubic function. What is an approximate zero of the function?



Use the drop-down menus to complete the statements.

A zero can be found between input values of
because
.

One zero of the function is approximately
.

Answer 1

I don't see the table — can you paste the input/output pairs (or upload the image)? I need those values to choose the correct interval and compute the approximate zero.

If you want to do it yourself, here’s how:

1. Find two consecutive input values a and b for which the outputs f(a) and f(b) have opposite signs (one positive, one negative). Then, by the Intermediate Value Theorem, a zero lies between a and b. So the drop-down sentence should read:
"A zero can be found between input values of a and b because f(a) and f(b) have opposite signs."

2. To approximate the zero, use linear interpolation (a quick estimate):
x ≈ a + (0 − f(a))*(b − a)/(f(b) − f(a)).
That gives "One zero of the function is approximately [that x]."

Example: if the table has f(1)=4 and f(2)=−2, then a=1, b=2 because 4 and −2 have opposite signs, and the approximate root is
x ≈ 1 + (0−4)*(2−1)/(−2−4) = 1 + (−4)/(-6) = 1 + 2/3 ≈ 1.667.

Send the table and I’ll fill in the exact choices and compute the approximation.