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Question Evaluate f(x)=(x−5)2f(x) = (x-5)^2 for given xx, then graph the function using (x,f(x))(x, f(x)) pairs.

Studdy Solution

STEP 1

Assumptions1. The function is given as f(x)=(x−5)f(x)=(x-5)^{} . We are given three values for xx:3,4, and53. We need to evaluate f(x)f(x) for each of these values of xx
4. The ordered pairs (x,f(x))(x, f(x)) will be used to graph the function

STEP 2

First, let's evaluate f(x)f(x) for x=x=. We do this by substituting x=x= into the function.
f()=(−5)2f() = (-5)^{2}

STEP 3

Now, calculate f(3)f(3).
f(3)=(3−5)2=(−2)2=f(3) = (3-5)^{2} = (-2)^{2} =

STEP 4

Next, evaluate f(x)f(x) for x=4x=4. We do this by substituting x=4x=4 into the function.
f(4)=(4−)2f(4) = (4-)^{2}

STEP 5

Now, calculate f(4)f(4).
f(4)=(4−5)2=(−1)2=1f(4) = (4-5)^{2} = (-1)^{2} =1

STEP 6

Finally, evaluate f(x)f(x) for x=5x=5. We do this by substituting x=5x=5 into the function.
f(5)=(5−5)2f(5) = (5-5)^{2}

STEP 7

Now, calculate f(5)f(5).
f(5)=(5−5)2=(0)2=0f(5) = (5-5)^{2} = (0)^{2} =0

STEP 8

We now have the ordered pairs (x,f(x))(x, f(x)) for each value of xx. They are1. (3,4)(3,4)2. (4,1)(4,1)3. (5,0)(5,0)These ordered pairs can be used to graph the function f(x)=(x−5)2f(x)=(x-5)^{2}.

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