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The table below represents a linear function f(x) and the equation represents a function g(x):

x f(x)
−1 −12 g(x)
0 −6 g(x) = 2x + 6
1 0

Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.

Respuesta :

Using linear function concepts, it is found that:

a) Function f(x) has a greater slope, that is, a greater rate of change, hence it increases faster than function g(x).

b) Due to the higher numeric value when x = 0, function g(x) has a greater y-intercept.

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), we have that:

  • When x changes by 1, y increases by 6, hence the slope is of 6.
  • When x = 0, y = -6, hence the y-intercept is of -6.

Function g(x) is defined by:

g(x) = 2x + 6.

Hence:

  • The slope is of 2.
  • The y-intercept is of 6.

Then:

a) Function f(x) has a greater slope, that is, a greater rate of change, hence it increases faster than function g(x).

b) Due to the higher numeric value when x = 0, function g(x) has a greater y-intercept.

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

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