# Unit 3_ Curve Sketching.pdf - Unit 3 Curve Sketching 1 Find...

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Unit 3: Curve Sketching 1. Find the intercepts of the function. a. ( x ) x 5 f = x 2 + 2 − 1
2. State the domain of the function.
b. x x 3 x 00 y = 4 3 + 7 2 − 1 + 1
Solution: ( x ) f = 2( x ) − 5 x − 5 ≥ 0 x ≥ 5 x ε R | x } D : { ≥ 5 3. Determine if the function is even, odd or neither. x
b. y = x 5 + x 3 + 7 f f
c. ( x ) f = 3 x + x 3 f
4. Determine the vertical asymptote(s). a. y = x +5 x −7 3 x −3 x −28 2 4 b. ( x ) f = x +2 x −5 x −6 3 2 = 2 5. Determine the horizontal asymptote. 2 -6 6 0
b. y = x −2 x +8 5 3 x +3 x + x −7 4 3 2 Horizontal asymptote: y = 0 Because the numerator has a degree lower than the denominator. c. y = 2 x 2 x +3 x −4 2 Dividing coefficients of the highest degrees by their terms. Horizontal asymptote: y = 1 2 = 2 6. For each function determine: i) the critical values ii) the intervals of increasing or decreasing iii) the maximum and minimum points. a. ( x ) x 2 x f = 4 2 + 1 − 7 3 3 3 3 1
b. ( x ) x 4 x 0 f = x 3 − 9 2 + 2 − 1