A comfy jacket is normally $200. It is on sale for 40% off. What is the sale price?
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To check if a piecewise defined function is continuous, you need to check how the pieces "glue" together when you step from one domain to the other.
So, the question is: what happens at x=3? If you reach x=3 from values slightly smaller than 3, you obey the rule f(x)=log(3x). So, as you approach 3, you get values closer and closer to
Similarly, if you reach x=3 from values slightly greater than 3, you obey the rule f(x)=(4-x)log(9). So, as you approach 3, you get values closer and closer to
So, the function is continuous at x=3, because both pieces approach log(9) as x approaches 3.
Explanation:
1. CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC — given
2. ∆CRH ~ ∆HSC — AA similarity theorem
3. ∠SCH ≅ ∠RHC — corresponding angles of similar triangles are congruent
4. CH ≅ HC — reflexive property of congruence
5. ∆CRH ≅ ∆HSC — SAS congruence theorem
6. CR ≅ HS — CPCTC
