Question

f is an even function. a = A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 3. Column 2 is labeled f (x) with entries 4, 5, a, 7. g is an odd function b = A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 3. Column 2 is labeled f (x) with entries b, 0, negative 3, negative 4.

Answer 1

The values of a and b are 4 and -3

How to solve for (a) and (b)?

To solve for a, we make use of the function f(x).

x    f(x)

2     4

0     5

2     a

3     7

Remove the x values 0 and 3

x    f(x)

2     4

2     a

The above table implies that:

f(2) = 4 and f(2) = a

Substitute 4 for f(2) in f(2) = a

4 = a

Rewrite as:

a = 4

To solve for b, we make use of the function g(x).

x    g(x)

2     b

0     0

2     -3

3     -4

Remove the x values 0 and 3

x    g(x)

2     b

2     -3

The above table implies that:

f(2) = b and f(2) = -3

Substitute -3 for f(2) in f(2) = b

-3 = b

Rewrite as:

b = -3

Hence, the values of a and b are 4 and -3

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Complete question

Use the Symmetry of a Function to Find Coordinates

f is an even function             g is an odd function

x    f(x)                                        x             g(x)

2     4                                          2              b

0     5                                          0              0

2     a                                          2              -3

3     7                                          3              -4

Find a and b