Math  /  Algebra

QuestionCurrent Attempt in Progress Are the two functions r(x)=2(x4)+10r(x)=2(x-4)+10 and s(x)=2x2s(x)=2 x-2 the same function?

Studdy Solution

STEP 1

1. We are given two functions r(x) r(x) and s(x) s(x) .
2. We need to determine if r(x) r(x) and s(x) s(x) are the same function by comparing their expressions.
3. The functions are considered the same if their expressions simplify to the same form.

STEP 2

1. Simplify the expression for r(x) r(x) .
2. Simplify the expression for s(x) s(x) .
3. Compare the simplified expressions of r(x) r(x) and s(x) s(x) .

STEP 3

Simplify the expression for r(x)=2(x4)+10 r(x) = 2(x-4) + 10 .
First, distribute the 2 inside the parentheses:
r(x)=2(x4)+10 r(x) = 2 \cdot (x - 4) + 10
r(x)=2x8+10 r(x) = 2x - 8 + 10
Combine like terms:
r(x)=2x+2 r(x) = 2x + 2

STEP 4

Simplify the expression for s(x)=2x2 s(x) = 2x - 2 .
Since the expression is already simplified, we have:
s(x)=2x2 s(x) = 2x - 2

STEP 5

Compare the simplified expressions of r(x) r(x) and s(x) s(x) .
r(x)=2x+2 r(x) = 2x + 2 s(x)=2x2 s(x) = 2x - 2
Since 2x+22x2 2x + 2 \neq 2x - 2 , we can conclude that r(x) r(x) and s(x) s(x) are not the same function.

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