I can't do these pre calc questions

Question

Answer 1

(20).

The value of x = 2 is always ≤ 3, so we can choose the function f(x) = x - 3.

To find the value of f(2), substitute x = 2 in the above function.

f(2) = (2) - 3 = - 1.

The value of f(2) = - 1.

 

Comments

How do you determine that x=2 is always ≤ 3? and why use f(x) = x -3 but not the other equations?

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From given two functions .

2 ≤ 3 is lies on first fuction only.

So we choose first function only.

Not to choose second function, since 2 is not greater than 3.

Answer 2

(21).

The parent function is f(x) = x².

The function f(x) = x² shifted two units to the left, then transformation equation is f(x - c) = f(x - 2) = (x - 2)².

The function f(x - c) = f(x - 2) = (x - 2)² shifted three units up, then transformation equation is f(x - c) + d = f(x - 2) + 3 = (x - 2)² + 3.

The transformation equation is (x - 2)² + 3.

Comments

How do you figure the first part out? Whenever I deal with this problem, I only use the transformation equation?

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