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QuestionFind the range of f(x)=2x−10f(x)=2^{x}-10 for integers xx from -1 to 3. Which values are in the range? Options: -12, -10, -9, -6, -2.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=x−10f(x)=^{x}-10 . The domain of f(x)f(x) is the set of integers from -1 to3

STEP 2

We need to find the range of f(x)f(x), which is the set of all possible output values. We can do this by substituting each value from the domain into the function and calculating the result.

STEP 3

First, let's substitute x=−1x=-1 into the function.
f(−1)=2−1−10f(-1)=2^{-1}-10

STEP 4

Calculate the value of f(−1)f(-1).
f(−1)=2−1−10=0.−10=−9.f(-1)=2^{-1}-10 =0. -10 = -9.

STEP 5

Next, let's substitute x=0x=0 into the function.
f(0)=20−10f(0)=2^{0}-10

STEP 6

Calculate the value of f(0)f(0).
f(0)=20−10=1−10=−9f(0)=2^{0}-10 =1 -10 = -9

STEP 7

Next, let's substitute x=1x=1 into the function.
f(1)=21−10f(1)=2^{1}-10

STEP 8

Calculate the value of f(1)f(1).
f(1)=21−10=2−10=−8f(1)=2^{1}-10 =2 -10 = -8

STEP 9

Next, let's substitute x=2x=2 into the function.
f(2)=22−f(2)=2^{2}-

STEP 10

Calculate the value of f(2)f(2).
f(2)=22−10=4−10=−6f(2)=2^{2}-10 =4 -10 = -6

STEP 11

Finally, let's substitute x=3x=3 into the function.
f(3)=3−10f(3)=^{3}-10

STEP 12

Calculate the value of f()f().
f()=2−10=8−10=−2f()=2^{}-10 =8 -10 = -2

STEP 13

Now, we have calculated all possible values of f(x)f(x) for the given domain. The range of f(x)f(x) is the set of these values −9.5,−9,−8,−6,−2-9.5, -9, -8, -6, -2.
From the given options, the elements of the range of f(x)f(x) are −9,−6,−2-9, -6, -2.

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