Question

A table with 2 columns and 7 rows. The first row, x, has the entries, negative 4, negative 3, negative 2, negative 1, 0, 1. The second row, y, has the entries, 0, negative 0.75, negative 1.50, negative 2.25, negative 3, negative 3.75 A table with 2 columns and 7 rows. The first row, x, has the entries, negative 4, negative 3, negative 2, negative 1, 0, 1. The second row, y, has the entries, negative 2.50, negative 2.50, negative 2.50, negative 2.50, negative 2.50, negative 2.50.
Determine which statements are true. Check all that apply.

h(x) has a constant output of –2.50.
As x increases, g(x) increases.
g(x) is greater than –2.50 for x values less than –1.
h(x) is less than –2.50 for x values greater than –2.
The input value for which g(x) = h(x) is between –1 and 0.

Answer 1

True:
- h(x) has a constant output of −2.50. (Every h value listed is −2.50.)
- g(x) is greater than −2.50 for x values less than −1. (For x = −4, −3, −2: g = 0, −0.75, −1.50, all > −2.50.)
- The input value for which g(x) = h(x) is between −1 and 0. (g(−1) = −2.25 > −2.50 and g(0) = −3 < −2.50, and the values follow an arithmetic pattern so g = −2.50 occurs at x = −2/3, which is between −1 and 0.)

False:
- As x increases, g(x) increases. (g decreases from 0 to −3.75 as x increases.)
- h(x) is less than −2.50 for x values greater than −2. (h = −2.50, not less than −2.50.)