Answer:
Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit
Step-by-step explanation:
The general form of the straight line equation is, y = m·x + c
Where;
m = The slope
c = The y-intercept
The parent function is, f(x) = x
The slope of the parent function, m₁ = 1
The y-intercept of the parent function, c₁ = 0
The x-intercept of the parent function = 0
The equation of the given function g(x) is derived as follows;
Two points on the line g(x) are (-2, 5) and (1, -4)
The slope of g(x), m₂ = (-4 - 5)/(1 - (-2)) = -3
The equation of g(x) is therefore;
y - 5 = -3 × (x - (-2)) = -3·x - 6
∴ y = -3·x - 6 + 5 = -3·x - 1
y = -3·x - 1
The slope of the given function, m₂ = -3
The y-intercept of the given function, c₂ = -1
The x-intercept of the function = -1
We have that a reflection of (x, y) across the y-axis gives (-x, y)
Therefore, the function g(x) is a reflection of f(x) across the y-axis
The slope of g(x) = -3 × The slope of f(x), therefore, g(x) is obtained by a vertical stretch of of f(x) by a factor of 3
The y-intercept of g(x) is lower than the y-intercept of g(x) by -1, therefore, f(x) is shifted down vertically by 1 unit to obtain g(x)
Therefore, the sequence of transformation that can be used to obtain g(x) from the parent function f(x) are;
Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit
