Created on 2024-06-20Asked by Isabella Jackson (Solvelet student)
Find the absolute value function of f(x)=3x−5 and evaluate it at x=−2.
Solution
Step 1: Define the absolute value function for f(x)=3x−5. The absolute value function is given by: f(x)={3x−5if 3x−5≥0−(3x−5)if 3x−5<0 Step 2: Determine the conditions. 3x−5≥0⟹x≥353x−5<0⟹x<35 Step 3: Express the absolute value function in piecewise form: f(x)={3x−5if x≥35−3x+5if x<35 Step 4: Evaluate f(x) at x=−2. Since −2<35: f(−2)=−3(−2)+5=6+5=11 Step 5: Conclusion. The absolute value function evaluated at x=−2 is f(−2)=11. Solved on Solvelet with Basic AI Model
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DefinitionAbsolute Value function: Absolute value function, 𝑓(𝑥) = |𝑥|, gives the non-negative value of 𝑥. Denoted as | 𝑥| = ⎩ ⎨ ⎧ 2 2 2 𝑥 if 𝑥 ≥0 −𝑥 if 𝑥<0. It measures the distance of ’’ 𝑥 ’’ from zero. Learn & solve absolute value functions with SolveletAI advanced step-by-step solutions. Generated instantly, learn and get explanations of the problem with the absolute value functions calculator at SolveletAI.
