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Math  /  Algebra

QuestionFind the function values given the function k(x)=∣x∣+3k(x)=|x|+3. Complete parts (a) through (f) below. a) k(0)=k(0)= □\square (Simplify your answer.) b) k(−5)=k(-5)= □\square (Simplify your answer.) c) k(5)=k(5)= □\square (Simplify your answer.) d) k(−10)=k(-10)= □\square (Simplify your answer.) e) k(a−3)=k(a-3)= □\square (Simplify your answer.) f) k(a+h)=k(a+h)= □\square (Simplify your answer.)

Studdy Solution

STEP 1

1. We are given the function k(x)=∣x∣+3 k(x) = |x| + 3 .
2. We need to evaluate this function at specific values and expressions for x x .

STEP 2

1. Evaluate k(x) k(x) at specific numerical values.
2. Simplify the expression for k(x) k(x) when x x is a variable expression.

STEP 3

Evaluate k(0) k(0) :
k(0)=∣0∣+3 k(0) = |0| + 3 k(0)=0+3 k(0) = 0 + 3 k(0)=3 k(0) = 3

STEP 4

Evaluate k(−5) k(-5) :
k(−5)=∣−5∣+3 k(-5) = |-5| + 3 k(−5)=5+3 k(-5) = 5 + 3 k(−5)=8 k(-5) = 8

STEP 5

Evaluate k(5) k(5) :
k(5)=∣5∣+3 k(5) = |5| + 3 k(5)=5+3 k(5) = 5 + 3 k(5)=8 k(5) = 8

STEP 6

Evaluate k(−10) k(-10) :
k(−10)=∣−10∣+3 k(-10) = |-10| + 3 k(−10)=10+3 k(-10) = 10 + 3 k(−10)=13 k(-10) = 13

STEP 7

Evaluate k(a−3) k(a-3) :
k(a−3)=∣a−3∣+3 k(a-3) = |a-3| + 3
This expression cannot be simplified further without knowing the value of a a .

STEP 8

Evaluate k(a+h) k(a+h) :
k(a+h)=∣a+h∣+3 k(a+h) = |a+h| + 3
This expression cannot be simplified further without knowing the values of a a and h h .
The function values are: a) k(0)=3 k(0) = 3 b) k(−5)=8 k(-5) = 8 c) k(5)=8 k(5) = 8 d) k(−10)=13 k(-10) = 13 e) k(a−3)=∣a−3∣+3 k(a-3) = |a-3| + 3 f) k(a+h)=∣a+h∣+3 k(a+h) = |a+h| + 3

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