Respuesta :
Answer:
g: y=±[tex]\frac{c^{2} }{4}x+c[/tex] where c is the y-intercept
Step-by-step explanation:
It is given that g is a vertical translation of a linear function.
Hence g is also a linear function with general equation:
[tex]y=mx+c[/tex]
The area of the triangle formed by a straight line with slope m and y-intercept c with x-axis and y-axis is given by the formula:
Δ = |[tex]\frac{c^{2} }{2m}[/tex]|
Given:area=2 sq units.
2=±[tex]\frac{c^{2} }{2m}[/tex]
∴ m=±[tex]\frac{c^{2} }{4}[/tex]
Putting m in the equation of straight line we get.
y=±[tex]\frac{c^{2}}{4}x+c[/tex] where c is the y-intercept.
Equations are used to show the relationship between related functions or variables.
The equation of g(x) is: [tex]g(x) = x + 2[/tex] or [tex]g(x) = x - 2[/tex]
The parent linear function is represented as:
[tex]f(x) = x[/tex]
The given area of the triangle is:
[tex]Area = 2[/tex]
The area of a triangle is calculated as:
[tex]Area = \frac{1}{2} bh[/tex]
So, we have:
[tex]\frac{1}{2} bh = 2[/tex]
Multiply both sides by 2
[tex]bh = 2 \times 2[/tex]
This means that the base and height of the triangle is 2
So, the equation of g(x) is:
[tex]g(x) = f(x) + 2[/tex] or [tex]g(x) = f(x) - 2[/tex]
[tex]g(x) = x + 2[/tex] or [tex]g(x) = x - 2[/tex]
Read more about functions and equations at:
https://brainly.com/question/22964920
