The equation for the functions g₁(x), g₂(x), and g₃(x) are (x + 3)², (x + 3)² + 5, and -[(x + 3)² + 5] respectively.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = x²
We have:
g₁(x) which is a transformed function of f(x)
f(x) shifted three units to the left.
Plug x → (x + 3)
g₁(x) = (x + 3)²
Similarly,
Equation for the function whose graph is in the shape of g₁(x), but shifted five units up.
g₂(x) = (x + 3)² + 5
Equation for the function whose graph is in the shape of g₂(x), but reflected in the x-axis.
g₃(x) = -[(x + 3)² + 5]
Thus, the equation for the functions g₁(x), g₂(x), and g₃(x) are (x + 3)², (x + 3)² + 5, and -[(x + 3)² + 5] respectively.
Learn more about the function here:
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