Question

The tables represent the functions f(x) and g(x).

A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, f(x), has the entries, negative 5, negative 3, negative 1, 1, 3, 5. A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, g(x), has the entries, negative 13, negative 9, negative 5, negative 1, 3, 7.
Which input value produces the same output value for the two functions?

x = –3
x = –1
x = 0
x = 1

Answer 1

To find the input value that produces the same output for both functions \( f(x) \) and \( g(x) \), we can compare the corresponding output values for \( f(x) \) and \( g(x) \) at the provided x-values.

Here are the outputs for both functions as per the tables:

For \( f(x) \):
- \( f(-3) = -5 \)
- \( f(-2) = -3 \)
- \( f(-1) = -1 \)
- \( f(0) = 1 \)
- \( f(1) = 3 \)
- \( f(2) = 5 \)

For \( g(x) \):
- \( g(-3) = -13 \)
- \( g(-2) = -9 \)
- \( g(-1) = -5 \)
- \( g(0) = -1 \)
- \( g(1) = 3 \)
- \( g(2) = 7 \)

Now we can analyze the outputs for the provided x-values:

1. For \( x = -3 \):
- \( f(-3) = -5 \)
- \( g(-3) = -13 \)
- Not equal.

2. For \( x = -1 \):
- \( f(-1) = -1 \)
- \( g(-1) = -5 \)
- Not equal.

3. For \( x = 0 \):
- \( f(0) = 1 \)
- \( g(0) = -1 \)
- Not equal.

4. For \( x = 1 \):
- \( f(1) = 3 \)
- \( g(1) = 3 \)
- Equal.

The input value that produces the same output value for the two functions is \( x = 1 \).