Question

Write a linear function f with the given valuesf(-1) = -6, f(4) = -6

Answer 1

Answer:

The linear function f with the given values f(-1) = -6, f(4) = -6 is:

f(x) = -6

Step-by-step explanation:

The given values are:

f(-1) = -6, f(4) = -6

This can be interpreted as:

x₁ = -1, f₁ = -6, x₂ = 4, f₂ = -6

The equation of a line is written as:

f - f₁ = m(x - x₁)

where m is the slope and is given by the formula:

`\begin{gathered} m=(f_2-f_1)/(x_2-x_1) \\ m=(-6-(-6))/(4-(-1)) \\ m=0 \end{gathered}`

Substitute f₁ = -6, m = 0, and x₁ = -1 into the equation f - f₁ = m(x - x₁)

f - (-6) = 0(x - (-1)

f + 6 = 0(x + 1)

f + 6 = 0

f = -6

The linear function f with the given values f(-1) = -6, f(4) = -6 is:

f(x) = -6