Processing math: 100%
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

4.4 E: Sketch the GRAPH Exercises

( \newcommand{\kernel}{\mathrm{null}\,}\)

4.4: Graphing Exercises

For the following exercises, draw a graph of the functions without using a calculator. Use the 9-step process for graphing from Class Notes and from the section 4.5 text.

The answers here are just the graph (step 9). Your solutions should have all steps with the information (intervals of incr/decr, local max/min, etc) as you see in the section 4.5 text examples.

294) y=3x2+2x+4

295) y=x33x2+4

Answer:
CNX_Calc_Figure_04_06_207.jpegNote: should have a hole at the point (-3,2)

296) y=2x+1x2+6x+5

297) y=x3+4x2+3x3x+9

Answer:
CNX_Calc_Figure_04_06_209.jpeg

298) y=x2+x2x23x4

299) y=x25x+4

Answer:
CNX_Calc_Figure_04_06_211.jpeg

300) y=2x16x2

301) y=cosxx, on x=[2π,2π]

Answer:
CNX_Calc_Figure_04_06_213.jpeg

302) y=exx3

303) y=xtanx,x=[π,π]

Answer:
CNX_Calc_Figure_04_06_215.jpeg

304) y=xln(x),x>0

305) y=x2sin(x),x=[2π,2π]

Answer:
CNX_Calc_Figure_04_06_217.jpeg

306) For f(x)=P(x)Q(x) to have an asymptote at y=2 then the polynomials P(x) and Q(x) must have what relation?

307) For f(x)=P(x)Q(x) to have an asymptote at x=0, then the polynomials P(x) and Q(x). must have what relation?

Answer:
Q(x). must have have xk+1 as a factor, where P(x) has xk as a factor.

308) If f(x) has asymptotes at y=3 and x=1, then f(x) has what asymptotes?

309) Both f(x)=1(x1) and g(x)=1(x1)2 have asymptotes at x=1 and y=0. What is the most obvious difference between these two functions?

Answer:
\(\displaystyle lim_{x→1^−f(x)and \displaystyle lim_x→1−g(x)

310) True or false: Every ratio of polynomials has vertical asymptotes.


For the following exercises, draw a graph of the functions without using a calculator. Use the 9-step process for graphing from Class Notes and from the section 4.4 text. Your solutions should have all steps with the information (intervals of incr/decr, local max/min, etc) as you see in the section 4.4 text examples.

J4.4.1) y=x2+2x24

J4.4.2) f(x)=x3x13

J4.4.3) f(x)=xlnx

Answer:
Domain (0, ∞); Intercept (0,1); Symmetry Not odd, Not even; VA none, HA none, as x → ∞ , f → ∞;
increasing on (1e,); decreasing on (0,1e); min (1e,1e); no max;
concave up (0, ∞); never concave down; no inflection point
clipboard_ef655da882d72bfeeeedae72b91510c20.png

J4.4.4) f(x)=x46x2

J4.4.5) f(x)=x2x2

Answer:
Domain x2 ; Intercept (0,0); Symmetry Not odd, Not even; VA x=2, HA none, as x , f; as x , f;
increasing on (,0) (4,,), decreasing on (0,2) (2,4); min (4,8); max;(0,0);
concave up (2, ∞), concave down (-∞ , 2); inflection points (2,222), (2,222)
clipboard_e4cda2768aa44fafed42d5484f506eeef.png

J4.4.6) f(x)=x22x4

J4.4.7) f(x)=4x13+x43

Answer:
Domain (-∞, ∞); Intercepts (-4,0) (0,0); Symmetry Not odd, Not even; VA none, HA none, as x± , f;
increasing on (1,); decreasing on (,1,); min (1,3); max none;
concave up (,0) (2,,); concave down (0, 2); inflection points (2,632)
clipboard_e2b8a32ac96a77f05f550765e88785376.png

J4.4.8) f(x)=1(1+ex)2

J4.4.9) f(x)=x+3x2+1

Answer:
Domain (-∞, ∞); Intercepts (-3,0), (0,3); Symmetry Not odd, Not even; VA none, HA y=1 (as x) , HA y=1 (as x);
increasing on (,13); decreasing on (13,); max (13,10); min none;
concave up (,12), (1,);concave down (12,1); inflection points (12,5), (1,22)
clipboard_e5ec445731c41315a4d22129d5fa9385d.png

4.4 E: Sketch the GRAPH Exercises is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by LibreTexts.

Support Center

How can we help?