In Exercises 45–48, let f(x) = (x - 2)2 + 1. Match the
function with its graph

45) The function corresponds to graph A

46) The function corresponds to graph C

47) The function corresponds to graph B

48) The function corresponds to graph D

Step-by-step explanation:

We know that the function f(x) is:

45)

The function g(x) is given by:

using f(x) we can find f(x-1)

If we take the derivative and equal to zero we will find the minimum value of the parabolla (x,y) and then find the correct graph.

Puting it on g(x) we will get y value.

Then, the minimum point of this function is (3,1) and it corresponds to (A)

46)

Let's use the same method here.

Let's find the first derivative and equal to zero to find x and y minimum value.

Evaluatinf g(x) at this value of x we have:

Then, the minimum point of this function is (0,1) and it corresponds to (C)

47)

Let's use the same method here.

Let's find the first derivative and equal to zero to find x and y minimum value.

Evaluatinf g(x) at this value of x we have:

Then, the minimum point of this function is (2,3) and it corresponds to (B)

48)

Let's use the same method here.

Let's find the first derivative and equal to zero to find x and y minimum value.

Evaluatinf g(x) at this value of x we have:

Then, the minimum point of this function is (2,-2) and it corresponds to (D)

I hope it helps you!

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