Question

each table of values represents a linear function. Determine the symbolic representation for each function (express you answer in slope-intercept form: f (x) = mx + b)

x f(x)
2 5
3 1

x g(x)
4 2
7 8

Answer 1

The linear functions in this problem are given as follows:

• f(x) = -4x + 13.

• g(x) = 2x - 6.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For function f(x), when x increases from 2 to 3, f(x) decays from 5 to 1, hence the slope is of -4 and:

f(x) = -4x + b.

When x = 2, f(x) = 5, hence the y-intercept is found as follows:

5 = -4(2) + b

b = 13.

Then:

f(x) = -4x + 13.

For function g(x), when x increases from 4 to 7, g(x) increases from 2 to 8, hence the slope is of:

m = (8 - 2)/(7 - 4) = 6/3 = 2.

Hence:

g(x) = 2x + b.

When x = 4, g(x) = 2, hence the y-intercept is found as follows:

2 = 2(4) + b

2 = 8 + b

b = -6.

Then:

g(x) = 2x - 6.

More can be learned about linear functions at https://brainly.com/question/24808124

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