Question

Given various values of the linear functions f(x) and g(x) in the table, determine the y-intercept of (f- g)(x).

Answer 1

The y-intercept of linear function (f- g)(x) is (0,9)

How to determine the y-intercept?

The table of values is given as:

x   -6 -4 -1 3 4

f(x) 15 11 5 -3 -5

g(x) -36 -26 -11 9 14

The equations of the functions is calculated using:

$y = \frac{y_2 -y_1}{x_2-x_1} * (x -x_1) + y_1$

So, we have:

$f(x) = \frac{11 -15}{-4 + 6} * (x + 6) + 15$

Evaluate

f(x) = -2x + 3

Also, we have:

$g(x) = \frac{-26 + 36}{-4 + 6} * (x + 6) - 36$

Evaluate

g(x) = 5x - 6

Next, we calculate (f - g)(x) using:

(f - g)(x) = f(x) - g(x)

This gives

(f - g)(x) = -2x + 3 - 5x + 6

Substitute 0 for x

(f - g)(0) = -2(0) + 3 - 5(0) + 6

Evaluate

(f - g)(0) = 9

Hence, the y-intercept of (f- g)(x) is (0,9)

Read more about linear functions at:

brainly.com/question/24896196

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