LECTURE NOTES: 4-5 CURVE SKETCHING PART 2) · 2021. 8. 18. · LECTURE NOTES: 4-5 CURVESKETCHING...
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L ECTURE N OTES : 4-5 C URVE S KETCHING ( PART 2) WARM UP PROBLEM Find your copy of the Graphing Guidelines! PRACTICE PROBLEMS 1. Sketch the curve y = x − 2 sin x on [−2π, 2π]. (a) Find the domain. (b) Find the x and y-intercepts. (c) Find the symmetries/ periodicity of the curve. (d) Determine the asymptotes. (e,f) Determine where the function is increasing/ decreasing and find the local maximum/ mini- mum values 1 Section 4-5 (part 2)
Transcript of LECTURE NOTES: 4-5 CURVE SKETCHING PART 2) · 2021. 8. 18. · LECTURE NOTES: 4-5 CURVESKETCHING...
LECTURE NOTES: 4-5 CURVE SKETCHING
(PART 2)
WARM UP PROBLEM Find your copy of the Graphing Guidelines!PRACTICE PROBLEMS
1. Sketch the curve y = x− 2 sinx on [−2π, 2π].
(a) Find the domain.
(b) Find the x and y-intercepts.
(c) Find the symmetries/ periodicity of the curve.
(d) Determine the asymptotes.
(e,f) Determine where the function is increasing/ decreasing and find the local maximum/ mini-mum values
1 Section 4-5 (part 2)
(g) Find the intervals of concavity/inflection points.
(h) Sketch the curve.
2 Section 4-5 (part 2)
2. Sketch the graph of f(x) =3x2
x2 + 4
(a) Find the domain.
(b) Find the x and y-intercepts.
(c) Find the symmetries/ periodicity of the curve.
(d) Determine the asymptotes.
(e,f) Determine where the function is increasing/ decreasing and find the local maximum/ mini-mum values
(g) Find the intervals of concavity/inflection points.
(h) Sketch the curve.
3 Section 4-5 (part 2)
3. Sketch the graph of f(x) = x√4− x2
(a) Find the domain.
(b) Find the x and y-intercepts.
(c) Find the symmetries/ periodicity of the curve.
(d) Determine the asymptotes.
(e,f) Determine where the function is increasing/ decreasing and find the local maximum/ mini-mum values
(g) Find the intervals of concavity/inflection points.
(h) Sketch the curve.
4 Section 4-5 (part 2)
4. Sketch the curve y =x√
9 + x2
(a) Find the domain.
(b) Find the x and y-intercepts.
(c) Find the symmetries/ periodicity of the curve.
(d) Determine the asymptotes.
(e,f) Determine where the function is increasing/ decreasing and find the local maximum/ mini-mum values
(g) Find the intervals of concavity/inflection points.
(h) Sketch the curve.
5 Section 4-5 (part 2)
5. Sketch the curve y =x3 + 4
x2
(a) Find the domain.
(b) Find the x and y-intercepts.
(c) Find the symmetries/ periodicity of the curve.
6 Section 4-5 (part 2)
(d) Determine the asymptotes. (Try to find the slant asymptote. That is, what line does thisfunction approach as x → ±∞?)
(e,f) Determine where the function is increasing/ decreasing and find the local maximum/ mini-mum values
(g) Find the intervals of concavity/inflection points.
(h) Sketch the curve.
7 Section 4-5 (part 2)
